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In this paper, a class of differential variational inequalities are studied, and a new approach is introduced to relax the convexity condition. Firstly, an existence theorem of Carathéodory weak solution for the differential variational inequalities is established. Secondly, an algorithm for solving the problem is developed and the convergence analysis for the algorithm is given. Finally, a numerical example is reported to illustrate the proposed algorithm. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a new iterative method that is the combination of the proximal point algorithm, viscosity approximation method and alternating resolvent method for finding the common zeros of two accretive operators in Banach spaces. And we will prove the strong convergence theorems for the iterative algorithms and give the example of the main theorems. The results of this paper are improvements and extensions of the corresponding ones announced by many others. [ABSTRACT FROM AUTHOR]

In this paper, we provide a novel fractional particle swarm optimization (FPSO) algorithm. The traditional PSO is one of the most well-known bio-inspired algorithms used in optimization problems, which basically consists of a number of particles that collectively move in search of the global optimum. Nevertheless, despite its success over the past 20 years, the PSO is also known to be unable to converge, and even stagnate, in many complex problems with multiple local optima. In order to overcome this drawback, this paper proposes a modified version of the PSO algorithm, considering a fractional calculus approach. Stability results evaluation is carried out to analytically prove the convergence of the fractional extensions. This is naturally followed by simulation results to test the fractional-based PSOs under several well-known objective functions, thus highlighting the relationship between the fractional order velocity and position of particles with the convergence of the algorithm. Experimental results show that the FPSO and its variants significantly outperform the traditional PSO. [ABSTRACT FROM AUTHOR]

This paper investigates the Pareto optimization scheduling problem on a single machine with two competing agents A and B in which agent A wants to minimize the number of tardy A -jobs and agent B wants to minimize the maximum cost of B -jobs. In the literature, the constrained optimization problem of minimizing the number of tardy A -jobs under the restriction that the maximum cost of B -jobs is bounded is solved in polynomial time. This implies that the corresponding Pareto optimization scheduling problem can be solved in a weakly polynomial time. In this paper, by presenting a new algorithm for the constrained optimization problem, we provide a strongly polynomial-time algorithm for the corresponding Pareto optimization scheduling problem. Experimentation results show that the proposed algorithm for the considered problem is efficient. [ABSTRACT FROM AUTHOR]

Air pollution models plays a critical role in atmospheric environment research. Chemical kinetic equations is an important component of air pollution models. The chemical equations is numerically sticky because of its stiffness, nonlinearity, coupling and nonnegativity of the exact solutions. Over the past decades, numerous papers about chemical equation solvers have been published. However, these solvers cannot preserve the nonnegativity of the exact solutions. Therefore, in the calculation, the negative numerical concentration values are usually set to zero artificially, which may cause simulation errors. To obtain real nonnegative numerical concentration values, very small step-size has to be adopted. Then enormous amount of CPU time is consumed to solve the chemical equations. In this paper, we revisit this topic and derive a new algorithm. Our algorithm Modified-Backward-Euler (MBE) Method can unconditionally preserve the nonnegativity of the exact solutions. MBE is a simple, robust and efficient solver. It is much faster and more precise than the traditional solvers such as LSODE and QSSA. The numerical results and parameter suggestions are shown at the end of the paper. MBE is based on the P-L structure of the chemical equations and a deeper view into the nature of Euler Methods. It cannot only be used to solve chemical equations, but can also be applied to conquer ordinary differential equations (ODEs) with similar P-L structure. [ABSTRACT FROM AUTHOR]

In this paper, we give some necessary and sufficient conditions for the consistence of the system of quaternion matrix equations A 1 X = C 1 , Y B 1 = D 1 , A 2 W = C 2 , Z B 2 = D 2 , A 3 V = C 3 , V B 3 = C 4 , A 4 V B 4 = C 5 , A 5 X + Y B 5 + C 6 W + Z D 6 + E 6 V F 6 = G 6 , and constitute an expression of the general solution to the system when it is solvable. The outcomes of this paper encompass some recognized results in the collected works. In addition, we establish an algorithm and a numerical example to illustrate the theory constructed in the paper. [ABSTRACT FROM AUTHOR]

Uncertain differential equation is a type of differential equation driven by canonical Liu process. How to obtain the analytic solution of uncertain differential equation has always been a thorny problem. In order to solve uncertain differential equation, early researchers have proposed two numerical algorithms based on Euler method and Runge–Kutta method. This paper will design another numerical algorithm for solving uncertain differential equations via Adams–Simpson method. Meanwhile, some numerical experiments are given to illustrate the efficiency of the proposed numerical algorithm. Furthermore, this paper gives how to calculate the expected value, the inverse uncertainty distributions of the extreme value and the integral of the solution of uncertain differential equation with the aid of Adams–Simpson method. [ABSTRACT FROM AUTHOR]

First of all, by characterizing solutions of the quaternion equation a x = x ˜ b , this paper studies consimilarity of quaternions and some related consequences. For the important role of coneigenvalues in consimilarity tranformations of quaternion matrices, this paper further derives the relations between principle right coneigenvalues of a quaternion matrix and eigenvalues of the corresponding real representation matrix. Then, based on the real representation matrix, an effective algorithm is presented to calculate all coneigenvalues and the associated coneigenvectors of a quaternion matrix. Finally, two numerical examples are given to verify the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

A given inventory problem consists of two parts: (1) the modeling part and (2) the solution procedure part. The modeling part can provide insight into the solution of the inventory problem and the solution procedure part involves the implementation of the inventory model. Both the modeling part and the solution procedure part of the inventory problem are equally important. Recently, Ouyang et al. [17] developed an integrated inventory model with a price-sensitive demand rate and determined both the economic lot size of the buyer’s ordering and the supplier’s production batch in order to maximize the total profit per unit time. Basically, their modeling is correct and interesting. They developed an algorithm based upon the first-order condition and the second-order condition to locate the optimal solution. However, the fundamentals of mathematics and the numerical examples which are considered in this paper illustrate that their algorithm based upon the first-order condition and the second-order condition to locate the optimal solution has several shortcomings. These shortcomings are shown here to influence the accuracy of the implementation of the inventory model. Since there exist reasons and motivations to present the correct solution procedures to the targeted readers, the main purpose of this paper is to adopt the rigorous methods of mathematical analysis in order to develop the complete solution procedures to locate the optimal solution for removing shortcomings in the earlier investigation by Ouyang et al. [17]. [ABSTRACT FROM AUTHOR]

The paper deals with the problem of power quality and its solution. Passive or active compensators are usually used to reduce distortions of voltage and current waveforms. Active power filters seem to be the best choice if the effect of compensation is the only criterion. However, the financial cost of such a solution put the potential investors off. The paper shows that the cost could be reduced considerably if the optimization of active power filter allocation, as well as their nominal currents, is carried out. Two cases have been considered – active power filters with a classical control algorithm, which operates locally and aims at obtaining sinusoidal shape of waveforms in the point of installation, and active power filters with a modified control algorithm, which aims at reduction of waveform distortions in all nodes of an analyzed power system. Goal functions and optimization problems for both cases have been defined. [ABSTRACT FROM AUTHOR]

This paper presents two conformance indexes that can be used to measure a similarity between two delineated structures. The authors use the presented conformance indexes for rating the results of Poisson Surface Reconstruction algorithm on real patient datasets. The rating is based on three delineations: original contours created during a standard procedure, reconstructed contours and reference contours created with an extra care by another physician. The chosen conformance indexes compare the delineations in two different forms: as a voxel grid and as a surface mesh. In this paper each of the conformance indexes is calculated in three different modes: the standard mode where all differences between datasets are taken into account and two more measuring how much one dataset exceeds the other. The last two modes are not symmetrical. The proposed conformance indexes allowed us to compare efficiently two delineations. The presented results also allow to state that the use of mesh reconstruction algorithms can improve delineations prepared within a limited time frame. [ABSTRACT FROM AUTHOR]

In this paper, neural algorithms, including the multi-layered perceptron (MLP) differential approximator, generalized hybrid power series, discrete Hopfield neural network, and the hybrid numerical, are used for constructing models that incorporate a priori knowledge in the form of differential equations for dynamic engineering processes. The properties of these approaches are discussed and compared to each other in terms of efficiency and accuracy. The presented algorithms have a number of advantages over other traditional mesh-based methods such as reduction of the computational cost, speed up of the execution time, and data integration with the a priori knowledge. Furthermore, the presented techniques are applicable when the differential equations governing a system or dynamic engineering process are not fully understood. The proposed algorithms learn to compute the unknown or free parameters of the equation from observations of the process behavior, hence a more precise theoretical description of the process is obtained. Additionally, there will be no need to solve the differential equation each time the free parameters change. The parallel nature of the approaches outlined in this paper make them attractive for parallel implementation in dynamic engineering processes. [ABSTRACT FROM AUTHOR]

In this paper, we present a new modified method for solving multi-level multi objective linear fractional programming problems (ML-MOLFPPs) based on fuzzy goal programming (FGP) approach with some modifications in the algorithm suggested by Baky (2010) [18] which dealt with multi-level multi objective linear programming problem (ML-MOLPP). In proposed modified approach, numerator and denominator function of each objective at each level are individually transformed into fuzzy goals and their aspiration levels are determined using individual best solutions. Different linear membership functions are defined for numerator and denominator function of each objective function. Then highest degree of each of these membership goals is achieved by minimising the sum of negative deviational variables. The proposed algorithm simplifies the ML-MOLFPP by eliminating solution preferences by the decision makers at each level, thereby avoiding difficulties associate with multi-level programming problems and decision deadlock situations. The aim of this paper is to present simple and efficient technique to obtain compromise optimal solution of ML-MOLFP problems. Numerical examples are illustrated in order to support the proposed modified FGP technique. [ABSTRACT FROM AUTHOR]

• A novel fractional gradient descent method with adaptive momentum is presented for training BP neural networks. • The convergence of the proposed algorithm is proved. • The proposed fractional algorithm can effectively improve the training performance and expand the selection range of learning rate. A novel fractional gradient descent method with adaptive momentum is presented in this paper to improve the convergence speed and stability for BP neural network training. The fractional Grünwald-Letnikov derivative is used for the fractional gradient. The coefficient of the momentum term is set as an adaptive variable, depending on the fractional gradient of the current step and the weight change of the previous step. We give a detailed convergence proof of the proposed method. Experiments on MNIST data sets and XOR problem demonstrate that the fractional gradient descent method with adaptive momentum term can effectively improve convergence speed, maintain stability of BP neural network training, help escape from local minimum points, and enlarge the selection range of the learning rate. [ABSTRACT FROM AUTHOR]

• A centrality model for urban street networks is proposed. • Non-local random walks are used to extend the Adapted PageRank Algorithm model. • The non-local movement of the random walker is more intuitive. In the urban street network domain, there is growing interest in extending conventional centrality measures to incorporate node-specific information (such as georeferenced socioeconomic data) in order to help identify important locations in an urban environment. One such centrality measure that is gaining attention is the Adapted PageRank Algorithm (APA) model. However, a fundamental concern with the APA model is the notion of teleportation because it means the random walker is equally likely to jump or 'teleport' to any intersection (node) in the street network, regardless of how far away it is. In this paper, we propose a centrality model that overcomes this counterintuitive idea. More specifically, we extend the APA model by modifying the jumping probabilities so that the random walker is more inclined to jump to a nearby intersection than a distant intersection. We accomplish this using non-local random walks which allow a random walker to jump to any node in the network with probabilities that depend on the distance separating the nodes. To demonstrate the differences between the two models, we present and discuss experimental results for a small ten node graph and a real-world urban street network. [ABSTRACT FROM AUTHOR]

• Deep insight on both sequential and parallel GMRES for linear systems. • Rich discussion on the convergence and acceleration of GMRES. • Brief account of other problems and block algorithms. This paper is about GMRES algorithms for the solution of nonsingular linear systems. We first consider basic algorithms and study their convergence. We then focus on acceleration strategies and parallel algorithms that are useful for solving challenging systems. We also briefly discuss other problems, such as systems with multiple right-hand sides, shifted systems, and singular systems. [ABSTRACT FROM AUTHOR]

In this paper we first write a proof of the perceptron convergence algorithm for the complex multivalued neural networks (CMVNNs). Our primary goal is to formulate and prove the perceptron convergence algorithm for the bicomplex multivalued neural networks (BMVNNs) and other important results in the theory of neural networks based on a bicomplex algebra. [ABSTRACT FROM AUTHOR]

• The variable elimination method is used to find the convex hull containing the concerned set of variables of interest. This generalizes the idea due to Madigan and Mosurski [1] to any undirected graphs. • We design a node absorbing algorithm based on variable elimination to find the convex hull containing the variables of interest in undirected graphs and give an analysis of the complexity of the proposed algorithm. • By analyzing the node absorbing algorithm, we propose a more efficient convex hull finding algorithm called inducing path absorbing algorithm, whose complexity is also analyzed. • We apply our proposed algorithm to a gene network and reduce the dimension from 31 to 6. • Our simulation demonstrates the proposed inducing path absorbing algorithm is efficient for realizing structural dimension reduction for complex networks with large scale. An undirected graphical model is a joint distribution family defined on an undirected graph, and the convex hull of a node set in the graph is the minimal convex subgraph containing it. It has been shown that a graphical model is collapsible onto the minimal local sub-model induced by the convex hull which contains variables of interest under Gaussian and multinomial distributions. This motivates many scholars to design algorithms for finding the unique convex hull containing nodes of interest in a graph. In this paper, we propose two algorithms called, respectively, the node absorption algorithm (NA) and the inducing path absorption algorithm (IPA), to find the minimal convex subgraph containing variables of interest in an undirected graph. These algorithms can be used as potential tools to find the minimal sub-model including variables of interest onto which a graphical model of large-scale can be collapsible. Experiments show that the proposed IPA significantly outperforms the NA and other existing algorithms. Furthermore, we apply the IPA to a gene network so as to collapse a large network onto a smaller network including the interested variables, and thus to achieve the aim of structural dimension reduction. [ABSTRACT FROM AUTHOR]

• The proposed Prox-NPGA can handle the non-smooth term in the objective function. • The convergences of CTA-Prox-NPGA and ATC-Prox-NPGA are proved. • The upper bounds of the step-sizes are given. • Prox-NPGA is not only an algorithm, but also an algorithmic framework. In this paper, we study a class of distributed constraint-coupled optimization problems, where each local function is composed of a smooth and strongly convex function and a convex but possibly non-smooth function. We design a novel proximal nested primal-dual gradient algorithm (Prox-NPGA), which is a generalized version of the exiting algorithm–NPGA. The convergence of Prox-NPGA is proved and the upper bounds of the step-sizes are given. Finally, numerical experiments are employed to verify the theoretical results and compare the convergence rates of different versions of Prox-NPGA. [ABSTRACT FROM AUTHOR]

• In Section 5 Preconditioned BiCOR and TCORS Algorithms are added, i.e., "PBiCOR" and "PTCORS", which are two main methods obtained by introducing the preconditioner based on the nearest Kronecker product in Loan and Pitsianis [28] to accelerate the proposed TBiCOR and TCORS methods in the previous version. • In "Numerical Experiments" section, we added "PBiCOR" and "PTCORS" and compared with other methods. Numerical examples show that PTCORS converges fastest among all methods listed, and PBiCOR converges a bit slower than PTCORS does. • We have added an acknowledgements part. Other sections, such as the title/ introduction/abstract/Numerical experiments/Conclusions section, are all updated. • We have checked the English usage of the revised paper carefully. In this paper, the preconditioned TBiCOR and TCORS methods are presented for solving the Sylvester tensor equation. A tensor Lanczos L -Biorthogonalization algorithm (TLB) is derived for solving the Sylvester tensor equation. Two improved TLB methods are presented. One is the biconjugate L -orthogonal residual algorithm in tensor form (TBiCOR), which implements the L U decomposition for the triangular coefficient matrix derived by the TLB method. The other is the conjugate L -orthogonal residual squared algorithm in tensor form (TCORS), which introduces a square operator to the residual of the TBiCOR algorithm. A preconditioner based on the nearest Kronecker product is used to accelerate the TBiCOR and TCORS algorithms, and we obtain the preconditioned TBiCOR algorithm (PTBiCOR) and preconditioned TCORS algorithm (PTCORS). The proposed algorithms are proved to be convergent within finite steps of iteration without roundoff errors. Several examples illustrate that the preconditioned TBiCOR and TCORS algorithms present excellent convergence. [ABSTRACT FROM AUTHOR]

The hybridization of Differential Evolution (DE) and Particle Swarm Optimization (PSO) have been well preferred over their individual effort in solving optimization problems. The way of applying DE and PSO in the hybridization process is a big deal to achieve promising solutions. Recently, they have been used simultaneously (i.e. in parallel) on different sub-populations of the same population, instead of applying them alternatively in series over the generation. An attempt is made in this paper to hybrid DE and PSO in parallel, under a ‘tri-population’ environment. Initially, the whole population (in increasing order of fitness) is divided into three groups – inferior group, mid group and superior group. Based on their inherent ability, DE is employed in the inferior and superior groups whereas PSO is used in the mid-group. This proposed method is named as DPD as it uses DE–PSO–DE on the sub-populations of the same population. Two more strategies namely Elitism (to retain the best obtained values so far) and Non Redundant Search (to improve the solution quality) have been incorporated in DPD cycle. The paper is designed with three major aims: (i) investigation of suitable DE-mutation strategies to support DPD, (ii) performance comparison of DPD over state-of-the-art algorithms through a set of benchmark functions and (iii) application of DPD to real life problems. Numerical, statistical and graphical analysis in this paper finally concludes the robustness of the proposed DPD. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new numerical algorithm for solving the Riesz tempered space fractional diffusion equation. The stability and convergence of the numerical scheme are discussed via the technique of matrix analysis. Finally, numerical experiments are performed to confirm the effectiveness of our numerical algorithm. [ABSTRACT FROM AUTHOR]

In this paper, an attempt has been made to estimate the biophysical parameters in an improved version of Morris–Lecar (M–L) neuron model in a noisy environment. To observe the influence of noisy stimulation in estimation procedure, a Gaussian white noise has been added to the membrane voltage of the model system. Estimation of the parameters has been investigated by a proposed algorithm. The denoising technique (local projection method) has been applied to reduce the influence of noisy stimuli and the effectiveness of the method is reported. The proposed scheme performs well for an excitable neuron model and provides good estimates between the estimated parameters and the actual values in a reasonable way. This approach can be used for parameter estimation for other nonlinear dynamical systems. [ABSTRACT FROM AUTHOR]

In this paper, we present an adaptive method for the TV-based model of three norms L q ( q = 1 2 , 1 , 2 ) for the image restoration problem. The algorithm with the L 2 norm is used in the smooth regions, where the value of |∇ u | is small. The algorithm with the L 1 2 norm is applied for the jumps, where the value of |∇ u | is large. When the value of |∇ u | is moderate, the algorithm with the L 1 norm is employed. Thus, the three algorithms are applied for different regions of a given image such that the advantages of each algorithm are adopted. The numerical experiments demonstrate that our adaptive algorithm can not only keep the original edge and original detailed information but also weaken the staircase phenomenon in the restored images. Specifically, in contrast to the L 1 norm as in the Rudin–Osher–Fatemi model, the L 2 norm yields better results in the smooth and flat regions, and the L 1 2 norm is more suitable in regions with strong discontinuities. Therefore, our adaptive algorithm is efficient and robust even for images with large noises. [ABSTRACT FROM AUTHOR]

Set partitions avoiding k -crossing and k -nesting have been extensively studied from the aspects of both combinatorics and mathematical biology. By using the generating tree technique, the obstinate kernel method and Zeilberger’s algorithm, Lin confirmed a conjecture due independently to the author and Martinez–Savage that asserts inversion sequences with no weakly decreasing subsequence of length 3 and enhanced 3-nonnesting partitions have the same cardinality. In this paper, we provide a bijective proof of this conjecture. Our bijection also enables us to provide a new bijective proof of a conjecture posed by Duncan and Steingrímsson, which was proved by the author via an intermediate structure of growth diagrams for 01-fillings of Ferrers shapes. [ABSTRACT FROM AUTHOR]

The coupled Gross–Pitaevskii system studied in this paper is an important mathematical model describing spin-1 Bose-Einstein condensate. We propose a linearized and decoupled compact finite difference scheme for the coupled Gross–Pitaevskii system, which means that only three tri-diagonal systems of linear algebraic equations at each time step need to be solved by using Thomas algorithm. New types of mass functional, magnetization functional and energy functional are defined by using a recursive relation to prove that the new scheme preserves the total mass, energy and magnetization in the discrete sense. Besides the standard energy method, we introduce an induction argument as well as a lifting technique to establish the optimal error estimate of the numerical solution without imposing any constraints on the grid ratios. The convergence order of the new scheme is of O ( h 4 + τ 2 ) in the L 2 norm and H 1 norm, respectively, with time step τ and mesh size h . Our analysis method can be used to high dimensional cases and other linearized finite difference schemes for the two- or three-dimensional nonlinear Schrödinger/Gross–Pitaevskii equations. Finally, numerical results are reported to test the theoretical results. [ABSTRACT FROM AUTHOR]

Polynomial chaos expansion (PCE) is widely used by engineers and modelers in various engineering fields for uncertainty analysis. The computational cost of full PCE is unaffordable for the “curse of dimensionality” of the expansion coefficients. In this paper, a new method for developing sparse PCE is proposed based on the diffeomorphic modulation under observable response preserving homotopy (D-MORPH) algorithm. D -MORPH is a regression technique, it can construct the full PCE models with model evaluations much less than the unknown coefficients. This technique determines the unknown coefficients by minimizing the least-squared error and an objective function. For the purpose of developing sparse PCE, an iterative reweighted algorithm is proposed to construct the objective function. As a result, the objective in D -MORPH regression is converted to minimize the ℓ 1 norm of PCE coefficients, and the sparse PCE is established after the proposed algorithm converges to the optimal value. To validate the performance of the developed methodology, several benchmark examples are investigated. The accuracy and efficiency are compared to the well-established least angle regression (LAR) sparse PCE, and results show that the developed method is superior to the LAR-based sparse PCE in terms of efficiency and accuracy. [ABSTRACT FROM AUTHOR]

In the present paper, the phenomenon of the vibrational resonance in a quantic oscillator that possesses a fractional order damping and is driven by both the low and the high frequency periodic signals is investigated, and the approximate theoretical expression of the response amplitude at the low-frequency is obtained by utilizing the method of direct partition of motions. Based on the definition of the Caputo fractional derivative, an algorithm for simulating the system is introduced, and the new method is shown to have higher precision and better feasibility than the method based on the Grünwald –Letnikov expansion. Due to the order of the fractional derivative, various new resonance phenomena are found for the system with single-well, double-well, and triple-well potential, respectively. Moreover, the value of fractional order can be treated as a bifurcation parameter, through which, it is found that the slowly-varying system can be transmitted from a bistability system to a monostabillity one, or from tristability to bistability, and finally to monostabillity. Unlike the cases of the integer-order system, the critical resonance amplitude of the high-frequency signal in the fractional system does depend on the damping strength and can be significantly affected by the fractional-order damping. The numerical results given by the new method is found to be in good agreement with the analytical predictions. [ABSTRACT FROM AUTHOR]

Identifying the influential spreaders in complex network is a very important topic, which is conducive to deeply understanding the role of nodes in the information diffusion and epidemic spreading among a population. To this end, in this paper, we propose a novel classified neighbors algorithm to quantify the nodal spreading capability and further to differentiate the influence of various nodes. Here, we believe that the contribution of different neighbors to their focal node is different, and then classify the neighbors of the focal node according to the removal order of the neighbor in the process of k -shell decomposition. By assigning different weights for each class of neighbors and summing up the neighbors’ contributions, the spreading capacity of the focal node can be accurately characterized. Through extensive simulation experiments over 9 real-world networks, the weight distribution of different types of neighbors has been optimized, and the results strongly indicate that the current algorithm has the higher ranking accuracy and differentiation extent when compared to other algorithms, such as degree centrality, k -shell decomposition method and mixed degree decomposition approach. Current results can help to greatly reduce the cost of sales promotion, considerably suppress the rumor dissemination and effectively control the outbreak of epidemics within many real-world systems. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce the Stancu type generalisation of Lupaş–Schurer operators based on ( p, q )-integers. We are concerned with the basic convergence of the constructed operators based on Korovkin’s type approximation theorem. Further, we obtain the rate of convergence for the new operators in terms of the modulus of continuity, with the help of functions of Lipschitz class and Peetre’s K-functionals. Then, we present three significant numerical mathematical algorithms. Finally, in order to confirm our theoretical results we obtain error estimation and illustrate the convergence of the ( p, q )-Lupaş–Schurer–Stancu operators to certain functions by using MATLAB. [ABSTRACT FROM AUTHOR]

In this paper, convergence capability of the conventional fractional order gradient methods (FOGMs) is analyzed and a new FOGM with guaranteed and faster convergence ability is proposed. In particular, we further consider the case that the derivative order varies between 1 and 2, and give some discussion on how to determine the derivative order in the algorithm settings. Simulation results from a number of numerical examples are provided to illustrate the approaches. [ABSTRACT FROM AUTHOR]

Despite matrix completion requiring the global solution of a non-convex objective, there are many computational efficient algorithms which are effective for a broad class of matrices. Based on these algorithms for matrix completion with given rank problem, we propose a class of two-stage iteration algorithms for general matrix completion in this paper. The inner iteration is the scaled alternating steepest descent algorithm for the fixed-rank matrix completion problem presented by Tanner and Wei (2016), the outer iteration is used two iteration criterions: the gradient norm and the distance between the feasible part with the corresponding part of reconstructed low-rank matrix. The feasibility of the two-stage algorithms are proved. Finally, the numerical experiments show the two-stage algorithms with shorting the distance are more effective than other algorithms. [ABSTRACT FROM AUTHOR]

This paper is devoted to a structured perturbation analysis of the symmetric algebraic Riccati equations by exploiting the symmetry structure. Based on the analysis, the upper bounds for the structured normwise, mixed and componentwise condition numbers are derived. Due to the exploitation of the symmetry structure, our results are improvements of the previous work on the perturbation analysis and condition numbers of the symmetric algebraic Riccati equations. Our preliminary numerical experiments demonstrate that our condition numbers provide accurate estimates for the change in the solution caused by the perturbations on the data. Moreover, by applying the small sample condition estimation method, we propose a statistical algorithm for practically estimating the condition numbers of the symmetric algebraic Riccati equations. [ABSTRACT FROM AUTHOR]

Given a set S of n line segments in the plane, we say that a region R ⊆ R 2 is a stabber for S if R contains exactly one endpoint of each segment of S . In this paper we provide optimal or near-optimal algorithms for reporting all combinatorially different stabbers for several shapes of stabbers. Specifically, we consider the case in which the stabber can be described as the intersection of axis-parallel halfplanes (thus the stabbers are halfplanes, strips, quadrants, 3-sided rectangles, or rectangles). The running times are O ( n ) (for the halfplane case), O ( n log  n ) (for strips, quadrants, and 3-sided rectangles), and O ( n 2 log  n ) (for rectangles). [ABSTRACT FROM AUTHOR]

• Active fault-tolerant strategy is introduced to distributed state estimation scheme. • Intermittent fault (IF) detector is designed and the detectability of IF is analyzed. • Estimation errors can remain the prescribed performance under the influence of IF. In this paper, the problem of distributed fault-tolerant state estimation is studied for stochastic systems over sensor networks with intermittent sensor faults. Compared with the traditional state estimation algorithms, the distinct advantage of fault-tolerant state estimation is that the estimator can keep good performance whether sensor faults occur or not. Different from the previous literature concerning with distributed fault diagnosis, the distributed fault diagnosis problem is investigated in this paper for intermittent faults, whose appearing time, disappearing time and magnitude are all nondeterministic. The distributed fault-tolerant state estimation scheme is constructed, in which the appearing time and disappearing time of intermittent faults are detected, intermittent faults are estimated and compensated. By means of the matrix inequality technique, the H ∞ performance of state estimation errors is guaranteed by properly choosing the estimator parameters. Finally, two examples are provided to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

• Discrete time Consensus Based Optimization (CBO) algorithm on a convex set is introduced. • The error between optimal value and consensus value is rigorously calculated and further extended from previous paper. • Portfolio optimization problem was solved using our proposed constrained CBO algorithm. In this paper, we propose a predictor-corrector type Consensus Based Optimization(CBO) algorithm on a convex feasible set. Our proposed algorithm generalizes the CBO algorithm in [11] to tackle a constrained optimization problem for the global minima of the non-convex function defined on a convex domain. As a practical application of the proposed algorithm, we study the portfolio optimization problem in finance. In this application, we introduce an objective function to choose the optimal weight on each asset in an asset-bundle, which yields the maximal expected returns given a certain level of risks. Simulation results show that our proposed predictor-corrector type model is successful in finding the optimal value. [ABSTRACT FROM AUTHOR]

• In this paper, the nonlinear fault detection observer is constructed and the observer gain function is derivated by choosing the novel Lyapunov functions. The predetermined estimation accuracy-dependent nonnegative function is introducing in the last step of recursive algorithm. • The threshold design problem is solved by suppressing the residual within the predetermined output estimation accuracy range during the implementation process of observer. • The tight thresholds ϵ and ϵ are predetermined under strategic designing scheme. It is straightforward to implement by comparison with the existing empirical or calculation methods of threshold. This paper presents an fault detection (FD) method for a class of uncertain nonlinear systems with unmatched nonlinear fault functions and disturbances. A recursive FD observer is designed with predetermined and small output estimation error. The nonlinear observer gain function is achieved by introducing predetermined output estimation accuracy-dependent nonnegative functions. Combining Lyapunov functions, it is shown that the absolute value of the residual signal is equal or lesser than tight threshold before fault occurrence. The FD scheme is proposed following fault detectability analysis, simulation example indicates the validity of the proposed method. [ABSTRACT FROM AUTHOR]

• Investigation of the performance of Boris-SDC as particle pusher in particle-in-cell code • Extension of Boris-SDC to relativistic regimes • Boris-SDC provides higher accuracy than Boris but computational cost is about the same The paper investigates two new use cases for the Boris Spectral Deferred Corrections (Boris-SDC) time integrator for plasma simulations. First, we show that using Boris-SDC as a particle pusher in an electrostatic particle-in-cell (PIC) code can, at least in the linear regime, improve simulation accuracy compared with the standard second order Boris method. In some instances, the higher order of Boris-SDC even allows a much larger time step, leading to modest computational gains. Second, we propose a modification of Boris-SDC for the relativistic regime. Based on an implementation of Boris-SDC in the RUNKO PIC code, we demonstrate for a relativistic Penning trap that Boris-SDC retains its high order of convergence for velocities ranging from 0.5 c to > 0.99 c. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates single-machine scheduling problems with piece-rate machine maintenance and interval constrained actual processing time. The actual processing time of a job is a general function of the normal job processing time and the position in job sequence, and it is required to restrict in given interval otherwise earliness or tardiness penalty should be paid. The maintenance duration studied in the paper is a time-dependent linear function. The objective is to find jointly the optimal frequency to perform maintenances and the optimal job sequence to minimize the total cost, which is a linear function of the makespan, total earliness and total tardiness. There is shown that the problem can be optimally solved in O(n 4) time. There is also shown that two special cases of the problem can be optimally solved by lower order algorithms. [Copyright &y& Elsevier]

Abstract: Multipoint iterative methods belong to the class of the most efficient methods for solving nonlinear equations. Recent interest in the research and development of this type of methods has arisen from their capability to overcome theoretical limits of one-point methods concerning the convergence order and computational efficiency. This survey paper is a mixture of theoretical results and algorithmic aspects and it is intended as a review of the most efficient root-finding algorithms and developing techniques in a general sense. Many existing methods of great efficiency appear as special cases of presented general iterative schemes. Special attention is devoted to multipoint methods with memory that use already computed information to considerably increase convergence rate without additional computational costs. Some classical results of the 1970s which have had a great influence to the topic, often neglected or unknown to many readers, are also included not only as historical notes but also as genuine sources of many recent ideas. To a certain degree, the presented study follows in parallel main themes shown in the recently published book (Petković et al., 2013) [53], written by the authors of this paper. [Copyright &y& Elsevier]

Abstract: In this paper we provide an extension of the classical Chaos game for IFSP. The paper is divided into two parts: in the first one, we discuss how to determine the integral with respect to a measure which is a combination of a self-similar measure from an IFSP along with a density given by an IFSM. In the second part, we prove a version of the Ergodic Theorem for the integration of a continuous multifunction with respect to the invariant measure of an IFSP. These results are in line with some recent extensions of IFS theory to multifunctions. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to study the strong convergence of the implicit and composite viscosity iteration schemes to a unique common fixed point of nonexpansive semigroups , which is a solution of some variational inequality under certain conditions. As a application, we apply the proposed iterative algorithm to the minimization problem of finding a optimality condition. The results of this paper extend some recent results. [Copyright &y& Elsevier]

Abstract: This paper is devoted to the identification of a pollution source in a river. A simple mathematical model of such a problem is given by a one-dimensional linear advection–dispersion–reaction equation with a right hand side spatially supported in a point (the source) and a time varying intensity, both unknown. There exist some identifiability results about this distributed system. But the numerical estimation of the unknown quantities require the introduction of an approximated model, whose identifiability properties are not analyzed usually. This paper has a double purpose: – to do the identifiability analysis of the differential system considered for estimating the parameters, – to propose a new numerical global search of these parameters, based on the previous analysis. Another consequence of this approach is to give the unknown pollution intensity directly as the solution of a differential equation. Lastly, the numerical algorithm is described in detail, completed with some applications. [Copyright &y& Elsevier]

• Firstly, a robust discrete-time non-smooth consensus protocol solves that consensus problem for the first-order leaderless multi-agent systems with external disturbance and discrete-time feedback. • Then, a discrete-time super-twisting observer is proposed to estimate the multi-agent systems disturbance. Combining the robust discrete-time non-smooth consensus protocol and discrete-time super-twisting observer, we get a new consensus protocol. The superiorities of this method contains two aspects, i.e., the disturbance rejection ability and a smaller consensus error. To the best authors' knowledge, the presented results in this paper are novel in the literature. In this paper, we firstly consider the consensus problems of first-order leaderless multi-agent systems with external disturbance. Then, we propose a robust discrete-time non-smooth (RDTNS) consensus protocol, which makes agents reach consensus within a region. Besides, we design a disturbance observer based on the discrete-time super-twisting algorithm (DTSTA), which can improve the disturbance rejection ability and decrease the consensus error for the multi-agent systems. At last, we get a robust discrete-time disturbance rejection control consensus protocol by combining the RDTNS consensus protocol with the discrete-time super-twisting observer (DTSTO). The simulation results verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

• It is the first time to investigate the problem of decentralized finite-time tracking control with prescribed settling time for a class of p -normal form stochastic large-scale systems with output interconnections existing in both the drift and diffusion terms. • It is the first time to investigate the connective stability problem for stochastic large-scale systems when the system structure changes. • Differing from the existing results, this paper proposes a new mathematical treatment algorithm to deal with the interconnections of stochastic large-scale systems, such that the decentralized tracking control is achieved. • The proposed control strategy is more convenient for practical application than the general finite-time control. • Due to the complexity of the system mathematics model, this paper can better reflect the application of mathematics. This paper aims to solve the decentralized finite-time connective tracking control problem for p -normal form stochastic large-scale systems with output interconnections existing in both the drift and diffusion terms. By means of the stochastic system theory and a prescribed finite-time performance function (PFTPF), a novel design scheme is presented for the decentralized finite-time connective tracking controllers with an arbitrarily prescribed settling time. The connective stability problem of stochastic large-scale systems is investigated for the first time. In addition, a new solution for the decentralized tracking control problem of stochastic large-scale systems is presented via a novel mathematical treatment algorithm. The proposed controllers can ensure that the tracking errors converge to a predetermined region within an arbitrarily prescribed settling time and the controlled system is connectively bounded stable in probability. Three simulation examples are presented to exhibit the performance and the superiority of the new control strategy. [ABSTRACT FROM AUTHOR]

• A novel online mode-free integral reinforcement learning algorithm is proposed to solve the mutiplayer non-zero sum games. • The online learning is used to compute the corresponding N coupled algebraic Riccati equations. • The policy iterative algorithm is applied to solve the coupled algebraic Riccati equations corresponding to the multiplayer nonzero sum games. In this paper, a novel online mode-free integral reinforcement learning algorithm is proposed to solve the multiplayer non-zero sum games. We first collect and learn the subsystems information of states and inputs; then we use the online learning to compute the corresponding N coupled algebraic Riccati equations. The policy iterative algorithm proposed in this paper can solve the coupled algebraic Riccati equations corresponding to the multiplayer non-zero sum games. Finally, the effectiveness and feasibility of the design method of this paper is proved by simulation example with three players. [ABSTRACT FROM AUTHOR]

• The problem of system tracking a single ROS is considered in the first part. The necessary and sufficient condition for the output tracking problem of PBCNs to be solvable is obtained. Based on this condition, the event-based controller has been designed to solve the considered tracking problem. Compared with [18,34], the number of control switchings for the designed controller can be reduced effectively. • A necessary and sufficient condition that the TVROT is trackable in probability one starting from the given initial state is obtained. Moreover, a new strategy is offered to design the control sequence. Compared with [31], we extend the necessary and sufficient condition that for the given initial state, the system can realize output tracking of TVROT from BNs to PBNs. • An effective algorithm is provided to solve the maximum tracking probability for the given initial state which can not track TVROT with probability one. Compared with [26], the problem of the system tracking a TVROT rather than a fixed ROS is considered in this paper, and time-variant controller has been designed to make the state of the system track TVROT from the given initial state with maximum probability. This paper mainly concentrates on the issue of finite-time output tracking of probabilistic Boolean control networks (PBCNs). Two kinds of problems are considered: (1) the system tracks a fixed reference output signal (ROS); (2) the system tracks a time variant reference output trajectory (TVROT). For the first problem, we design an effective event-triggered controller to realize output tracking in probability one. An algorithm is offered to find the control invariant subset (CIS) of a set, and a triggering set sequence is constructed based on the CIS. Next, a necessary and sufficient condition is proposed to judge whether the system is trackable in probability one. For the second problem, a criterion is given to judge whether the initial state can generate TVROT with probability one and an algorithm is then provided to solve the corresponding control sequence. Furthermore, a profit function is established to solve the maximum tracking probability for the initial state which can not generate TVROT with probability one. Lastly, two examples are offered to explain the theoretical results. [ABSTRACT FROM AUTHOR]

• We in this paper propose the bi-conjugate gradient and bi-conjugate residual methods in their tensor forms for solving the Sylvester tensor equation. • BiCG-BTF and BiCR-BTF methods are superior to the modified conjugate gradient method in terms of both the number of iteration steps and CPU time. • From the nearest Kronecker product, the convergence rate of the preconditioned BiCG-BTF and BiCR-BTF methods is about twice that of the PGMRES-BTF method. This paper is concerned with solving high order Sylvester tensor equation arising in control theory. We propose the tensor forms of the bi-conjugate gradient and bi-conjugate residual methods for solving the tensor equation. To improve their performance, two preconditioned iterative algorithms based on the nearest Kronecker product are developed for finding its solution. We also prove that the proposed algorithms are convergent to an exact solution within finite iteration steps for any initial tensor in the absence of round-off errors. At last, some numerical examples are provided to illustrate the feasibility and validity of the algorithms proposed. [ABSTRACT FROM AUTHOR]

Abstract: Very recently, Yao et al. (2010) [4] proposed a hybrid iterative algorithm. Under the parameter sequences satisfying some quite restrictive conditions, they derived a strong convergence theorem in a Hilbert space. In this paper, under the weaker conditions, we prove the strong convergence of the sequence generated by their iterative algorithm to a common fixed point of an infinite family of nonexpansive mappings, which solves a variational inequality. An appropriate example, such that all conditions of this result that are satisfied and that other conditions are not satisfied, is provided. Moreover, the method of our paper is different from the method in Yao et al. (2010) [4]. [Copyright &y& Elsevier]

In this paper, we propose a fuzzy SV- k -modes algorithm that uses the fuzzy k -modes clustering process to cluster categorical data with set-valued attributes. In the proposed algorithm, we use Jaccard coefficient to measure the dissimilarity between two objects and represent the center of a cluster with set-valued modes. A heuristic update way of cluster prototype is developed for the fuzzy partition matrix. These extensions make the fuzzy SV- k -modes algorithm can cluster categorical data with single-valued and set-valued attributes together and the fuzzy k -modes algorithm is its special case. Experimental results on the synthetic data sets and the three real data sets from different applications have shown the efficiency and effectiveness of the fuzzy SV- k -modes algorithm. [ABSTRACT FROM AUTHOR]