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This paper studies linear stochastic approximation (SA) algorithms and their application to multiagent systems in engineering and sociology. As main contribution, we provide necessary and sufficient conditions for convergence of linear SA algorithms to a deterministic or random final vector. We also characterize the system convergence rate, when the system is convergent. Moreover, differing from non-negative gain functions in traditional SA algorithms, this paper considers also the case when the gain functions are allowed to take arbitrary real numbers. Using our general treatment, we provide necessary and sufficient conditions to reach consensus and group consensus for first-order discrete-time multiagent system over random signed networks and with state-dependent noise. Finally, we extend our results to the setting of multidimensional linear SA algorithms and characterize the behavior of the multidimensional Friedkin–Johnsen model over random interaction networks. [ABSTRACT FROM AUTHOR]

This paper considers the constrained consensus problem over multi-cluster networks. It is assumed that the agents’ states are constrained by different sets, where each constraint set is privately known by the corresponding agent. Within this framework, a hierarchical projection-based consensus algorithm is presented to solve the considered problem. Technically, the consensus analysis of the proposed algorithm consists of the following three aspects: First, by using the property of the projection operator, the limiting behaviors of the agents’ states generated by the algorithm are investigated. Then, based on the limiting behaviors, it is proven that the agents’ states in the whole network achieve a constrained consensus. Furthermore, by introducing an important auxiliary variable that relates to the agents’ states, the linear convergence of the proposed algorithm is proved. Compared with the existing results, this paper generalizes the constrained consensus methods under single-cluster networks to the multi-cluster ones. Finally, simulations are given to verify the theoretical results. [ABSTRACT FROM AUTHOR]

By introducing the real linear operator, this paper offers a finite iterative algorithm for solving the complex generalized coupled Sylvester matrix equations. The properties of this algorithm are discussed and the finite convergence of this algorithm is proven. This algorithm unifies some finite iterative algorithms proposed by the earlier papers. Two numerical examples are offered to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Many-objective problems refer to the optimization problems containing more than three conflicting objectives. To obtain a representative set of well-distributed non-dominated solutions close to Pareto front in the objective space remains a challenging problem. Many papers have proposed different Multi-Objective Evolutionary Algorithms to solve the lack of the convergence and diversity in many-objective problems. One of the more promising approaches uses a set of reference points to discriminate the solutions and guide the search process. However, this approach was incorporated mainly in Multi-Objective Evolutionary Algorithms, and there are just some few promising adaptations of Particle Swarm Optimization approaches for effectively tackling many-objective problems regarding convergence and diversity. Thus, this paper proposes a practical and efficient Many-Objective Particle Swarm Optimization algorithm for solving many-objective problems. Our proposal uses a set of reference points dynamically determined according to the search process, allowing the algorithm to converge to the Pareto front, but maintaining the diversity of the Pareto front. Our experimental results demonstrate superior or similar performance when compared to other state-of-art algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we study the interacting multiple model (IMM) estimator for networked control systems with packet loss but without packet acknowledgment (ACK). The ACK is a signal sent by the actuator to inform the estimator of whether control packets are lost or not. A system with ACK is usually called a transmission control protocol (TCP) like system; otherwise, it is called a user datagram protocol (UDP) like system. We show that the stability of the IMM estimator for UDP-like systems is determined by the observation packet arrival rate (p.a.r.) and is independent of the control p.a.r. and control inputs. The IMM estimator is stable if the observation p.a.r. is greater than a critical value. We show that this critical value is the same as the critical value for the stability of the optimal estimator for its corresponding TCP-like system. If control inputs eventually tend to zero, the error covariance of the IMM estimator converges to that of the optimal estimator for TCP-like systems. We characterize the impact of the control/observation p.a.r. and the control input on estimation performance. Finally, we prove that the average estimation performance of the IMM estimator approximates that of the optimal estimator within a finite bound, and is superior to that of the linear minimum mean square error estimator. [ABSTRACT FROM AUTHOR]

Abstract The affine projection (AP) algorithm is one of the most celebrated adaptive filtering algorithms, and it achieves a good tradeoff between the convergence rate and computational complexity. However, the complexity of the AP algorithm increases with the projection order. A wealth of fast AP algorithms have been proposed to reduce the complexity in the last two decades. However, those low-complexity methods have not been well analyzed and compared. To fill this gap, this paper reviews the fast AP algorithms, including both fast filtering approaches and efficient solutions of the linear system of equations. The advantages and disadvantages of each fast implementation version are clarified based on an extensive performance evaluation, which could be useful to engineers when selecting a suitable algorithm for their specific applications and could also be a starting point for experts in this field to develop better solutions. [ABSTRACT FROM AUTHOR]

Abstract This paper develops a novel algorithm to solve real-world constrained optimization problems, which hybridizes multiobjective optimization techniques with an ϵ-constrained method. First, a constrained optimization problem at hand is transformed into a bi-objective optimization problem. By the transformation, the advantage of multiobjective optimization techniques can be utilized in the constrained optimization area to balance population diversity and convergence. Meanwhile, the ϵ-constrained method is applied, which keeps the population evolving toward feasible region of the constrained optimization problem. In our proposed algorithm, the differential evolution is employed as a search engine to create offspring at each generation. Further, different combinations of mutation operators have been developed to improve the search ability and the population convergence at different stages. The performance of our approach is evaluated on 64 benchmark test functions from three popular test suits. Experimental results demonstrate that our proposed approach is capable of obtaining high-quality solutions on the majority of benchmark test functions, when compared with some other state-of-the-art constrained optimization algorithms. [ABSTRACT FROM AUTHOR]

Highlights • The robustness of our solver is proved for fully incompressible 2D–3D FSI problems. • A partitioned smoother to a monolithic GMRES is more robust than a partitioned solver. • An algorithm for the direct-to-steady-state FSI problem is proposed. • Our formulation solved with the MUMPS package shows a very good convergence rate. Abstract In this paper we study a monolithic Newton–Krylov solver with exact Jacobian for the solution of fully incompressible Fluid-Structure Interaction problems of either steady-state or time-dependent type. Unlike common approaches, the enforcement of the incompressibility conditions both for the fluid and for the solid parts is taken care of by using an inf-sup stable finite element pair, without stabilization terms. The Krylov solver is preconditioned using geometric multigrid with smoothers of Richardson type, in turn preconditioned by additive Schwarz algorithms. The separate solution of fluid or solid operators occurs only at the preconditioning stage of the smoother, thus guaranteeing at each level an accurate interface momentum balance. The definition of the subdomains in the Schwarz smoother is driven by the natural splitting between fluid and solid. For each part and level, the domain is subdivided into a number of minimally overlapping subdomains. Numerical investigations of two and three-dimensional benchmark tests with Newtonian fluids and nonlinear hyperelastic solids are carried out by reporting several performance indices, including condition number estimates. A robust performance of the proposed fully incompressible solver is observed, especially for the more challenging direct-to-steady-state problems. [ABSTRACT FROM AUTHOR]

In this paper, the linear quadratic Nash games for infinite horizon nonstandard multiparameter singularly perturbed systems (MSPS) without the nonsingularity assumption that is needed for the existing result are discussed. The new strategies are obtained by solving the generalized cross-coupled multiparameter algebraic Riccati equations (GCMARE). Firstly, the asymptotic expansions for the GCMARE are newly established. The main result in this paper is that the proposed algorithm which is based on the Newton's method for solving the GCMARE guarantees the quadratic convergence. In fact, the simulation results show that the proposed algorithm succeed in improving the convergence rate dramatically compared with the previous results. It is also shown that the resulting controller achieves O(∥ μ ∥2n) approximation of the optimal cost. [ABSTRACT FROM AUTHOR]

This paper presents a nonhomogeneous continuous super-twisting algorithm for systems of relative degree more than one. The conditions of finite-time convergence to the origin are obtained and the robustness of the designed algorithm is discussed. The paper concludes with numerical simulations illustrating performance of the designed algorithms. [ABSTRACT FROM AUTHOR]

In addition to implicitly resolving the velocity pressure coupling at interior faces, it is also critical for a coupled solver to implicitly resolve this coupling for boundary faces. Failure to account for this leads to substantial degradation in the convergence characteristics of the solver. In this paper, details on the implicit treatment of boundary conditions for a coupled solver are presented in the context of the OpenFOAM ® framework. The boundary conditions presented include two geometric conditions namely, cyclicMMI and symmetry condition and a number of physical boundary conditions (inlet, outlet, and wall). The treatment is illustrated with modification to the boundary element coefficients and its effectiveness demonstrated for the case of “NASA Rotor 37”, a standard validation case. [ABSTRACT FROM AUTHOR]

“ Fuzzy Theoretic Approach to Signals and Systems ” assumes all system variables and parameters as uncertain (i.e. being characterized by membership functions), develops a mathematical theory for analytically determining the membership functions on system variables and parameters, derives algorithms for estimating the parameters of membership functions, and establishes robustness and convergence properties of the estimation algorithms. The membership functions are analytically determined via solving a variational optimization problem that maximizes the “ over-uncertainties-averaged-log-membership ” of the observed data around an initial guess. This paper develops the analytical fuzzy theory for the particular case of a multi-input single-output static system affected by noises. The theory facilitates designing an adaptive filtering algorithm. The robustness of the adaptive filtering algorithm is proved theoretically via a mathematical analysis. Numerical experiments further demonstrate the robustness of the filtering algorithm. A comparison of the algorithm with the state-of-art methods is made using the practical biomedical applications related to the modeling and analysis of heart rate signals for assessing the physiological state of an individual. [ABSTRACT FROM AUTHOR]

Various real-world applications can be formulated as feature selection problems, which have been known to be NP-hard. In this paper, we propose an effective feature selection method based on firefly algorithm (FFA), called return-cost-based binary FFA (Rc-BBFA). The proposed method has the capability of preventing premature convergence and is particularly efficient attributed to the following three aspects. An indicator based on the return-cost is first defined to measure a firefly’s attractiveness from other fireflies. Then, a Pareto dominance-based strategy is presented to seek the attractive one for each firefly. Finally, a binary movement operator based on the return-cost attractiveness and the adaptive jump is developed to update the position of a firefly. The experimental results on a series of public datasets show that the proposed method is competitive in comparison with other feature selection algorithms, including the traditional algorithms, the GA-based algorithm, the PSO-based algorithm, and the FFA-based algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we propose sparse adaptive channel estimation algorithms based on a mixed controlled l 2 and l p -norm error criterion and zero attracting theory. In the proposed algorithms, a controlling parameter within the range of [0, 1] is adopted to control the mixture of the l 2 and l p norms which are exerted on the estimation error. The sparsity-aware characteristic is implemented by an l 1 -norm penalty, a correntropy-induced metric penalty and a log-sum function constraint which are to exploit the in-nature sparseness of the channels. The proposed sparsity-aware algorithms give desired zero attractors in their iterations to speed up the convergence. The derivation of the proposed algorithms is presented in detail. We can find that the previously proposed sparsity-aware algorithms can be regarded as a special case of the proposed sparse adaptive algorithms. Also, the behaviors of the proposed algorithms are well verified over a multi-path wireless communication channel. As a result, our proposed algorithms are superior to the previously reported sparse mixed adaptive filters with respect to both the convergence and steady-state error for handling sparse signals. [ABSTRACT FROM AUTHOR]

Purpose – To improve the performance of the krill herd (KH) algorithm, in this paper, a series of chaotic particle-swarm krill herd (CPKH) algorithms are proposed for solving optimization tasks within limited time requirements. The paper aims to discuss these issues. Design/methodology/approach – In CPKH, chaos sequence is introduced into the KH algorithm so as to further enhance its global search ability. Findings – This new method can accelerate the global convergence speed while preserving the strong robustness of the basic KH. Originality/value – Here, 32 different benchmarks and a gear train design problem are applied to tune the three main movements of the krill in CPKH method. It has been demonstrated that, in most cases, CPKH with an appropriate chaotic map performs superiorly to, or at least highly competitively with, the standard KH and other population-based optimization methods. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses the convergence and stability analysis for iterative processes such as numerical iterative algorithms by using a novel trajectory distance based approach. Iterative dynamics are widespread in distributed algorithms and numerical analysis. However, efficient analysis of convergence and sensitivity of iterative dynamics is quite challenging due to the lack of systematic tools. For instance, the trajectories of iterative dynamics are usually not continuous with respect to the initial condition. Hence, the classical dynamical systems theory cannot be applied directly. In this paper, a trajectory distance based Lyapunov approach is proposed as a means to tackling convergence and sensitivity to the initial condition of iterative processes. Technically the problem of convergence and sensitivity is converted into finiteness of trajectory distance and semistability analysis of discrete-time systems. A semidefinite Lyapunov function based trajectory distance approach is proposed to characterize convergence and semistability of iterative dynamics. Three examples are provided to elucidate the proposed method. Finally, the proposed framework is used to solve the convergence and stability of iterative algorithms developed for balanced resource allocation and damage mitigation problems under adversarial attacks. [Copyright &y& Elsevier]

Abstract: Most real world multi-objective problems (MOPs) have a complicated solution space. Facing such problems, a direction vectors based co-evolutionary multi-objective optimization algorithm (DVCMOA) that introduces the decomposition idea from MOEA/D to co-evolutionary algorithms is proposed in this paper. It is novel in the sense that DVCMOA applies the concept of direction vectors to co-evolutionary algorithms. DVCMOA first divides the entire population into several subpopulations on the basis of the initial direction vectors in the objective space. Then, it solves MOPs through the co-evolutionary interaction among the subpopulations in which individuals are classified according to their direction vectors. Finally, it explores the less developed regions to maintain the relatively uniform distribution of the solution space. In this way, DVCMOA has advantages in convergence, diversity and uniform distribution of the non-dominated solution set, which are explained through comparison with other state-of-the-art multi-objective optimization evolutionary algorithms (MOEAs) in this paper. DVCMOA is shown to be effective on 6 multi-objective 0–1 knapsack problems. [Copyright &y& Elsevier]

Abstract: The research on optimal design of infinite-impulse response (IIR) filters based on optimization techniques has gained much attention in recent years. However, due to the limited performance of the applied optimization techniques, the orders of the filters, which can be obtained, are very low in the previous research. Memetic algorithms (MAs) are widely recognized to have better convergence capability than their conventional counterparts. However, the universality of the MAs, e.g. the ability of solving diverse kinds of digital IIR filter designs, is still limited. In this paper, we design a Two-Stage ensemble Memetic Algorithm (TSMA) framework to more appropriately synthesize the strengths of the evolutionary global search and local search techniques. In the first optimization stage, a competition is held among the candidate local search techniques. Its major idea is to choose the best local search technique and to obtain good initial state. Inheriting the good information of the first stage, the second optimization stage is to implement effective adaptive MA to pursue high-quality solution. The experimental studies presented in this paper contain three aspects: (1) the benefits of the TSMA framework are experimentally investigated by comparing TSMA with its sub-optimizers and recent effective evolutionary algorithms (EAs) on 26 test functions; then (2) TSMA is compared with 4 MAs on the CEC05 functions to comprehensively show the advantages of TSMA; and (3) the TSMA and 6 state-of-the-art algorithms are applied to design high-order digital infinite-impulse response (IIR) filters. The experimental results definitely demonstrate the excellent effectiveness, efficiency and reliability of TSMA on both function optimization and digital IIR filter design tasks. [Copyright &y& Elsevier]

In this paper we obtain the rates of convergence of the algorithms given in [13] and [14] for an automatic computation of the centered Hausdorff and packing measures of a totally disconnected self-similar set. We evaluate these rates empirically through the numerical analysis of three standard classes of self-similar sets, namely, the families of Cantor type sets in the real line and the plane and the class of Sierpinski gaskets. For these three classes and for small contraction ratios, sharp bounds for the exact values of the corresponding measures are obtained and it is shown how these bounds automatically yield estimates of the corresponding measures, accurate in some cases to as many as 14 decimal places. In particular, the algorithms accurately recover the exact values of the measures in all cases in which these values are known by geometrical arguments. Positive results, which confirm some conjectural values given in [13] and [14] for the measures, are also obtained for an intermediate range of larger contraction ratios. We give an argument showing that, for this range of contraction ratios, the problem is inherently computational in the sense that any theoretical proof, such as those mentioned above, might be impossible, so that in these cases, our method is the only available approach. For contraction ratios close to those of the connected case our computational method becomes intractably time consuming, so the computation of the exact values of the packing and centered Hausdorff measures in the general case, with the open set condition, remains a challenging problem. [ABSTRACT FROM AUTHOR]

This paper proposes a parameter estimation-based coupling control for the generalized cascade systems with uncertain parameters, where the single driven system is actuated by the multi-driving subsystems, resulting in the complicated coupling problem of output tracking and subsystems synchronization. To address this issue, a prescribed performance function (PPF) is firstly incorporated with the filtered representation of the driven system dynamics to design the adaptive parameter law, which maintains the finite-time parameter estimation with the prescribed performances. Then, the desired position of each driving subsystem is proposed to attain the driven system tracking with the sub-guaranteed cost, which is employed for the generalized coupling error (GCE) design to convert the complicated coupling issue into the GCE convergence, such that the complexity of controller design is extremely simplified. By applying the Chebyshev neural network (CNN), a novel integral sliding mode controller is presented to successfully eliminate the reaching phase and guarantee the finite-time GCE convergence with the suboptimal time. For the nonlinearity compensation, the novel learning law is derived to lessen the computational cost, where only a scalar weight needs to be updated online for each output of CNN. Finally, the comparative experiments illustrate the benefits of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Recently, several convergence rate results for Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) have been presented in the literature. In this paper, we show global linear convergence rate bounds for Douglas-Rachford splitting and ADMM under strong convexity and smoothness assumptions. We further show that the rate bounds are tight for the class of problems under consideration for all feasible algorithm parameters. For problems that satisfy the assumptions, we show how to select step-size and metric for the algorithm that optimize the derived convergence rate bounds. For problems with a similar structure that do not satisfy the assumptions, we present heuristic step-size and metric selection methods. [ABSTRACT FROM PUBLISHER]

Dissimilarity measures play a key role in exploring the inherent cluster structure of the data for any partitional clustering algorithm. Commonly used dissimilarity functions for clustering purpose are so far confined to the Euclidean, exponential and Mahalanobish distances. In this article we develop generalized algorithms to solve the partitional clustering problems formulated with a general class of Inner Product Induced Norm (IPIN) based dissimilarity measures. We provide an in-depth mathematical analysis of the underlying optimization framework and analytically address the issue of existence of a solution and its uniqueness. In absence of a closed form solution, we develop a fast stochastic gradient descent algorithm and the Minimization by Incremental Surrogate Optimization (MISO) algorithm (in case of constrained optimization) with exponential convergence rate to obtain the solution. We carry out a convergence analysis of the fuzzy and k -means clustering algorithms with the IPIN based dissimilarity measures and also establish how these algorithms guarantee convergence to a stationary point. In addition, we investigate the nature of the stationary point. Novelty of the paper lies in the introduction of a generalized class of divergence measures, development of fuzzy and k -means clustering algorithms with the general class of divergence measures and a thorough convergence analysis of the developed algorithms. [ABSTRACT FROM AUTHOR]

In order to improve the filter׳s performance when identifying sparse system, this paper develops two sparse-aware algorithms by incorporating the l 0 -norm constraint of the weight vector into the conventional normalized subband adaptive filter (NSAF) algorithm. The first algorithm is obtained from the principle of the minimum perturbation; and the second one is based on the gradient descent principle. The resulting algorithms have almost the same convergence and steady-state performance while the latter saves computational complexity. What׳s more, the performance of both algorithms is analyzed by resorting to some assumptions commonly used in the analyses of adaptive algorithms. Simulation results in the context of sparse system identification not only demonstrate the effectiveness of the proposed algorithms, but also verify the theoretical analyses. [ABSTRACT FROM AUTHOR]

This paper first discusses the inherent instability of the interpolating moving least squares (IMLS) method. In the original IMLS method, non-scaled polynomial bases are used. Theoretical and numerical results indicate that the stability of the original IMLS method decreases as the separation distance decreases. Then, using shifted and scaled polynomial bases, a stabilized algorithm of the IMLS method is proposed and analyzed. As an application, the stabilized IMLS method is finally introduced into the meshless Galerkin boundary node method (GBNM) to produce a stabilized GBNM for potential problems and Stokes problems. Numerical examples are given to demonstrate the stability and convergence of the presented stabilized algorithms. [ABSTRACT FROM AUTHOR]

The least mean p th power (LMP) and normalized LMP (NLMP) algorithms of adaptive Volterra filter have been successfully developed for nonlinear system identification in α -stable noise environments. However, there exists an inherent tradeoff between the convergence rate and steady-state performance. To address this compromise, a collaborative adaptive Volterra filter based on the convex combination scheme is proposed under the α -stable noise in this paper. By utilizing the convex combination which performs at least as well as the best component filter, the proposed algorithms achieve fast convergence rate and small misadjustment. Furthermore, by following a frame of the generalized combination scheme, two novel combination structures of Volterra filter are presented. Simulations in nonlinear system identification contexts demonstrate that the performances of the proposed algorithms are superior to the existing algorithms under the α -stable noise in terms of the convergence speed and steady state kernel error. [ABSTRACT FROM AUTHOR]

The symmetric solutions of linear matrix equations are extensively required in mathematics and engineering problems. The purpose of this paper is on deriving the biconjugate residual (BCR) algorithm for finding the least Frobenius norm symmetric solution pair ( X , Y ) of the coupled generalized Sylvester matrix equations { A 1 XB 1 + C 1 XD 1 + E 1 YF 1 = G 1 , A 2 XB 2 + C 2 XD 2 + E 2 YF 2 = G 2 . The convergence analysis shows that the BCR algorithm can compute the least Frobenius norm symmetric solution pair of the coupled generalized Sylvester matrix equations within a finite number of iterations in the absence of round-off errors. Finally, we give three numerical examples to illustrate the performance of the BCR algorithm. [ABSTRACT FROM AUTHOR]

Numerical simulations of high strain rate plastic flow have historically been built in a hypoelastic framework and use radial return (Wilkins’ method) as the solution algorithm. We show how each of these choices can lead to inaccurate and possibly nonconvergent results. We describe an alternative solution procedure based on a simple multiple time scale perturbation theory that is stable, accurate, computationally efficient and simple to implement. Further extension of these results then leads to a strain space formulation that has additional computational advantages. We illustrate our development with numerical experiments. This paper is dedicated to my friend and colleague Christo Christov on the occasion of his 60th birthday, in recognition of his many important and creative contributions to the formulation of continuum mechanics. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, two pivotal quantities are modified to construct prediction intervals for future lifetime based on random number of three parameters Weibull distribution, which can be widely applied in reliability theory and lifetime problems. The case of fixed sample size is presented as a special case. The random number has one of three important distributions as special cases. An algorithm is constructed to explain the importance of the theoretical results in applications. Simulation studies are conducted to investigate the efficiency of the purposed results. Finally, two numerical examples for real lifetime data are presented to illustrate the paper. [Copyright &y& Elsevier]

Abstract: Motivated by the recent success of diverse approaches based on differential evolution (DE) to solve constrained numerical optimization problems, in this paper, the performance of this novel evolutionary algorithm is evaluated. Three experiments are designed to study the behavior of different DE variants on a set of benchmark problems by using different performance measures proposed in the specialized literature. The first experiment analyzes the behavior of four DE variants in 24 test functions considering dimensionality and the type of constraints of the problem. The second experiment presents a more in-depth analysis on two DE variants by varying two parameters (the scale factor F and the population size NP), which control the convergence of the algorithm. From the results obtained, a simple but competitive combination of two DE variants is proposed and compared against state-of-the-art DE-based algorithms for constrained optimization in the third experiment. The study in this paper shows (1) important information about the behavior of DE in constrained search spaces and (2) the role of this knowledge in the correct combination of variants, based on their capabilities, to generate simple but competitive approaches. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers connections between the cost functions of some parameter identification methods for system modelling, including the well known projection algorithm, stochastic gradient (SG) algorithm and recursive least squares (RLS) algorithm, and presents a modified SG algorithm by introducing the convergence index and a multi-innovation projection algorithm, a multi-innovation SG algorithm and a multi-innovation RLS algorithm by introducing the innovation length, aiming at improving the convergence rate of the SG and RLS algorithms. Furthermore, this paper derives an interval-varying multi-innovation SG and an interval-varying multi-innovation RLS algorithm in order to deal with missing data cases. [Copyright &y& Elsevier]

An adaptive filtering algorithm is proposed in this paper to remove I/Q mismatch, dc offsets, flicker noise, and intersymbol interference (ISI) simultaneously in a direct-conversion receiver. I/Q mismatch is cancelled by a real valued adaptive mismatch canceller, and dc offsets are removed with one complex tap. In addition, flicker noise is modeled as a complex autoregressive (AR) random process so the system to be identified transforms to an ARX model. After estimating the coefficients in the model during the training period, the desired signal can be estimated using the decision feedback method. To accelerate the convergence of the algorithm and to reduce the estimation variance, an internal iterative algorithm is introduced. The convergence analysis of the proposed algorithm is also given, and the closed form of the minimum mean square error of the proposed algorithm is derived. Simulation results are provided to verify the superior performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Purpose - This paper seeks to develop an adaptive finite volume algorithm, and to present an extensive numerical analysis of it. Design/methodology/approach - The effectiveness of the developed algorithm is demonstrated through practical and computationally challenging problems. The algorithm is tested for a wide range of singularities. Findings - The convergence of the presented algorithm is independent of the regularity of the problems. It is shown that the our algorithm produces more accurate and well conditioned matrix systems. Research limitations/implications - Though the presented algorithm works for extreme singularities on rectangular meshes, it may not be as efficient if the underlying meshes are distorted, and it may not converge. Further research is under way for including the multi-point approximation technique into the algorithm. Practical implications - Almost all reservoir simulators use the two-point method, and this algorithm is based on this method. The algorithm can be easily incorporated into the reservoir simulators. The results show that such an implementation will greatly improve the computational efficiency of the simulators. The work is useful for computational scientists, and especially for the researchers in oil industries. The paper reports the numerical work with practical applications. Originality/value - The paper develops an adaptive finite volume algorithm. It is shown that adaptive meshes represent the underlying problem more accurately, and matrix systems associated with adaptive meshes are easier to solve compared with matrix systems associated with uniform meshes. [ABSTRACT FROM AUTHOR]

Abstract: The least mean p-norm (LMP) algorithm is an effective algorithm for processing the signal of α-stable distribution. This paper proposes data block adaptive filtering algorithms for the α-stable random processes based on the fractional lower order statistics (FLOS). The data block algorithms change the direction of coefficient increment vector by introducing a matrix which includes the information of more past input signal vectors than which are used in the LMP algorithm during the iteration process, taking full advantage of the past values of the gradient vector during the adaptation. Simulations studies indicate that the proposed algorithms increase convergence rate in non-Gaussian stable distribution noise environments compared to the existing algorithms based on FLOS summarized in this paper. [Copyright &y& Elsevier]

In this paper, we propose an algorithm for real-time signal processing of convolutive blind source separation (CBSS), which is a promising technique for acoustic source separation in a realistic environment, e.g., room/office or vehicle. First, we apply an overlap-and-save (sliding windows with overlapping) strategy that is most suitable for real-time CBSS processing; this approach can also aid in solving the permutation problem. Second, we consider the issue of separating sources in the frequency domain. We introduce a modified correlation matrix of observed signals and perform CBSS by diagonalization of the matrix. Third, we propose a method that can diagonalize the modified correlation matrix by solving a so-called normal equation for CBSS. One desirable feature of our proposed algorithm is that it can solve the CBSS problem explicitly, rather than stochastically, as is done with conventional algorithms. Moreover, a real-time separation of the convolutive mixtures of sources can be performed. We designed several simulations to compare the effectiveness of our algorithm with its counterpart, the gradient-based approach. Our proposed algorithm displayed superior convergence rates relative to the gradient-based approach. We also designed an experiment for testing the efficacy of the algorithm in real-time CBSS processing aimed at separating acoustic sources in realistic environments. Within this experimental context, the convergence time of our algorithms was substantially faster than that of the gradient-based algorithms. Moreover, our algorithm converges to a much lower value of the cost function than that of the gradient-based algorithm, ensuring better performance. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents an analysis of an adaptive random search (ARS) algorithm, a global minimization method. A probability model is introduced to characterize the statistical properties of the number of iterations required to find an acceptable solution. Moreover, based on this probability model, a new stopping criterion is introduced to predict the maximum number of iterations required to find an acceptable solution with a pre-specified level of confidence. Finally, this paper presents a systematic procedure for choosing the user-specified parameters in the ARS algorithm for fastest convergence. The results, which are valid for search spaces of arbitrary dimensions, are illustrated on a simple three-dimensional example. [Copyright &y& Elsevier]

The paper addresses the problem of identification of nonlinear characteristics in a certain class of discrete-time block-oriented systems. The systems are driven by random stationary white processes (independent and identically distributed input sequences) and disturbed by stationary, white, or colored random noise. The prior information about nonlinear characteristics is nonparametric. In order to construct identification algorithms, the orthogonal wavelets of compact support are applied, and a class of wavelet-based models is introduced and examined. It is shown that under moderate assumptions, the proposed models converge almost everywhere (in probability) to the identified nonlinear characteristics, irrespective of the noise model. The rule for optimum model-size selection is given and the asymptotic rate of convergence of the model error is established. It is demonstrated that, in some circumstances, the wavelet models are, in particular, superior to classical trigonometric and Hermite orthogonal series models worked out earlier. [ABSTRACT FROM AUTHOR]

Structure learning is a very important problem in the field of Bayesian networks (BNs). It is also an active research area for more than 2 decades; therefore, many approaches have been proposed in order to find an optimal structure based on training samples. In this paper, a Particle Swarm Optimization (PSO)-based algorithm is proposed to solve the BN structure learning problem; named BNC-PSO ( B ayesian N etwork C onstruction algorithm using PSO ). Edge inserting/deleting is employed in the algorithm to make the particles have the ability to achieve the optimal solution, while a cycle removing procedure is used to prevent the generation of invalid solutions. Then, the theorem of Markov chain is used to prove the global convergence of our proposed algorithm. Finally, some experiments are designed to evaluate the performance of the proposed PSO-based algorithm. Experimental results indicate that BNC-PSO is worthy of being studied in the field of BNs construction. Meanwhile, it can significantly increase nearly 15% in the scoring metric values, comparing with other optimization-based algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we will introduce the reconstruction of variational iteration method (RVIM) to solve multi-order fractional differential equations (M-FDEs), which include linear and nonlinear ones. We will easily obtain approximate analytical solutions of M-FDEs by means of the RVIM based on the properties of fractional calculus. Moreover, the convergence of proposed method will be shown. Our scheme has been constructed for the fully general set of M-FDEs without any special assumptions, and is easy to implement numerically. Therefore, our method is more practical and helpful for solving a broad class of M-FDEs. Numerical results are carried out to confirm the accuracy and efficiency of proposed method. Several numerical examples are presented in the format of table and graphs to make comparison with the results that previously obtained by some other well known methods. [ABSTRACT FROM AUTHOR]

The asymptotic stability of distributed-event triggered control for large-scale interconnected systems can be achieved with time-dependent trigger functions. The choice of some of the parameters in the trigger functions relies on some properties of the overall system, which are not known a priori by the individual nodes. This paper presents an iterative method for the distributed estimation of such parameters, which allows the event-triggered control algorithm to evolve to a less conservative design. We provide proofs of convergence while the asymptotic stability and the existence of a lower bound for the inter-event times are preserved. The complexity of the proposed approach is analyzed, and the results are illustrated through simulations. [ABSTRACT FROM AUTHOR]

In this paper, a dynamic mentoring scheme along with a self-regulation scheme have been incorporated in the standard Particle Swarm Optimization (PSO) algorithm to empower the searching particles with human-like characteristics. The algorithm is referred to as a Dynamic Mentoring and Self-Regulation based Particle Swarm Optimization (DMeSR-PSO) algorithm. Based on their experiences, the particles are divided into three groups, viz., the mentor group, the mentee group and the independent learner group where the number of particles in each group is dynamically changing in every iteration. In human learning psychology, mentoring is regarded as a powerful and effective learning process and independent learners are the ones who do not need mentoring and are capable of performing self-regulation of their own knowledge. Therefore, the particles in each of the above three groups have different learning strategies for their velocity updates where the mentors are equipped with a strong self-belief based search, the mentees are taking guidance from the mentors and the independent learners employ self-perception strategy. The DMeSR-PSO algorithm has been extensively evaluated using the simple unimodal and multimodal benchmark functions from CEC2005, more complex shifted and rotated benchmark functions fromCEC2013 and also based on eight real- world problems from CEC2011. The results have been compared with six state-of-the-art PSO variants and five meta-heuristic algorithms for the CEC2005 problems. Further, a comparative analysis on CEC2013 benchmark functions with different PSO variants has also been presented. Finally, DMeSR-PSO's performance on the real-world problems is compared with the top two algorithms from the CEC2011 competition. The results indicate that the proposed learning strategies help DMeSR-PSO to achieve faster convergence and provide better solutions in most of the problems with a 95% confidence level, yielding an effective optimization algorithm for real-world applications. [ABSTRACT FROM AUTHOR]

This paper proposes a novel diffusion subband adaptive filtering algorithm for distributed networks. To achieve a fast convergence rate and small steady-state errors, a variable step size and a new combination method is developed. For the adaptation step, the upper bound of the mean-square deviation (MSD) of the algorithm is derived and the step size is adaptive by minimizing it in order to attain the fastest convergence rate on every iteration. Furthermore, for a combination step realized by a convex combination of the neighbor-node estimates, the proposed algorithm uses the MSD, which contains information on the reliability of the estimates, to determine combination coefficients. Simulation results show that the proposed algorithm outperforms the existing algorithms in terms of the convergence rate and the steady-state errors. [ABSTRACT FROM AUTHOR]

Recently, krill herd algorithm (KHA) is proposed for the solution of global optimization problem. Various chaotic maps are considered in the proposed chaotic KHA (CKHA) of the present work to improve the performance of basic KHA method. It is observed that Logistic map based CKHA offers better results as compared other chaotic maps. The performance of the proposed CKHA is tested on standard 26-bus and IEEE 57-bus test power systems for the solution of optimal power flow of power system with different objectives that reflect minimization of fuel cost or active power loss or sum of total voltage deviation. Results obtained by using CKHA are compared to other evolutionary optimization techniques surfaced in the recent state-of-the-art literature. The results presented in this paper show that the proposed CKHA algorithm outperforms the other techniques in terms of convergence rate and global search ability. [ABSTRACT FROM AUTHOR]

The Normalized Least Mean Square (NLMS) algorithm with a filtered-x structure (FxNLMS) is a widely used adaptive algorithm for Active Noise Control (ANC) due to its simplicity and ease of implementation. One of the major drawbacks is its slow convergence. A modified filtered-x structure (MFxNLMS) can be used to moderately improve the speed of convergence, but it does not offer a huge improvement. A greater increase in the speed of convergence can be obtained by using the MFxNLMS algorithm with orthogonal correction factors (M-OCF), but the usage of orthogonal correction factors also increases the computational complexity and limits the usage of the M-OCF in massive real-time applications. However, Graphics Processing Units (GPUs) are well known for their potential for highly parallel data processing. Therefore, GPUs seem to be a suitable platform to ameliorate this computational drawback. In this paper, we propose to derive the M-OCF algorithm to a partitioned block-based version in the frequency domain (FPM-OCF) for multichannel ANC systems in order to better exploit the parallel capabilities of the GPUs. The results show improvements in the convergence rate of the FPM-OCF algorithm in comparison to other NLMS-type algorithms and the usefulness of GPU devices for developing versatile, scalable, and low-cost multichannel ANC systems. [ABSTRACT FROM AUTHOR]

A consensus problem consists of a group of dynamic agents who seek to agree upon certain quantities of interest. This problem can be generalized in the context of convex metric spaces that extend the standard notion of convexity. In this paper we introduce and analyze a randomized gossip algorithm for solving the generalized consensus problem on convex metric spaces, where the communication between agents is controlled by a set of Poisson counters. We study the convergence properties of the algorithm using stochastic calculus. In particular, we show that the distances between the states of the agents converge to zero with probability one and in the r^th mean sense. In the special case of complete connectivity and uniform Poisson counters, we give upper bounds on the dynamics of the first and second moments of the distances between the states of the agents. In addition, we introduce instances of the generalized consensus algorithm for several examples of convex metric spaces together with numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we consider the multi-dimensional Kesten algorithm studied in Xu and Dai (2012). The convergence in r th mean for the algorithm is established under the weaker assumptions than Xu and Dai (2012). Moreover, we obtain also the almost sure convergence of the algorithm under the conditions of Xu and Dai (2012). [ABSTRACT FROM AUTHOR]

In a recent paper, we investigated the uniform convergence of Lagrange interpolation at the zeros of the orthogonal polynomials with respect to a Freud-type weight in the presence of constraints. We show that by a simple procedure it is always possible to transform the matrices of these zeros into matrices such that the corresponding Lagrange interpolating polynomial with respect to the given constraints well approximates a given function. Here, starting from the interest to construct a suitable interpolation operator with a preassigned node, we introduce an algorithm that allows us to obtain new matrices. For the Lagrange operator related to these new matrices that have the preassigned node among their elements, we prove results about the optimal rate of convergence as well as we apply successfully this method to some applications. [ABSTRACT FROM AUTHOR]

Several techniques have been proposed in the literature to accelerate the convergence of adaptive algorithms for the identification of sparse impulse responses (i.e., with energy concentrated in a few coefficients). Among these techniques, the improved µ-law proportionate normalized least mean squares (IMPNLMS) algorithm is one of the most effective. This paper presents an accurate transient analysis of this algorithm and derives an estimate of its steady-state MSE, without requiring the assumption of white Gaussian input signals. [ABSTRACT FROM AUTHOR]

In this paper, we provide the almost-sure convergence and the asymptotic normality of a smooth version of the Robbins-Monro algorithm for the quantile estimation. A Monte Carlo simulation study shows that our proposed method works well within the framework of a data stream. [ABSTRACT FROM AUTHOR]

Nonnegative matrix factorization (NMF) has recently become a very popular unsupervised learning method because of its representational properties of factors and simple multiplicative update algorithms for solving the NMF. However, for the common NMF approach of minimizing the Euclidean distance between approximate and true values, the convergence of multiplicative update algorithms has not been well resolved. This paper first discusses the convergence of existing multiplicative update algorithms. We then propose a new multiplicative update algorithm for minimizing the Euclidean distance between approximate and true values. Based on the optimization principle and the auxiliary function method, we prove that our new algorithm not only converges to a stationary point, but also does faster than existing ones. To verify our theoretical results, the experiments on three data sets have been conducted by comparing our proposed algorithm with other existing methods. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with a finite-time particle swarm optimization algorithm for odor source localization. First, a continuous-time finite-time particle swarm optimization (FPSO) algorithm is developed based on the continuous-time model of the particle swarm optimization (PSO) algorithm. Since the introduction of a nonlinear damping item, the proposed continuous-time FPSO algorithm can converge over a finite-time interval. Furthermore, in order to enhance its exploration capability, a tuning parameter is introduced into the proposed continuous-time FPSO algorithm. The algorithm’s finite-time convergence is analyzed by using the Lyapunov approach. Second, the discrete-time FPSO algorithm is obtained by using a given dicretization scheme. The corresponding convergence condition is derived by using a linear matrix inequality (LMI) approach. Finally, the features and performance of the proposed FPSO algorithm are illustrated by using two ill-posed functions and twenty-five benchmark functions, respectively. In numerical simulation results, the problem of odor source localization is presented to validate the effectiveness of the proposed FPSO algorithm. [Copyright &y& Elsevier]