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The paper is focused on the numerical analysis of the two-point inverse stationary heat flow problem, namely the identification of the thermal load. Determination of selected parameters is possible on the basis of temperature measurements, done at specified few locations. This problem may be modelled as the optimization problem, standard numerical analysis of which requires multiple solutions of boundary value problems. However, the novel solution approach, proposed here, is based on the well-known concept of the Monte Carlo method with an appropriate random walk technique. It yields explicit stochastic relations combining computed temperatures and all load parameters. Such relations may be directly applied in most standard optimization algorithms, replacing time-consuming solutions of systems of algebraic equations. Moreover, one may construct the semi-analytical approach, in which the unknown load parameters are obtained explicitly, allowing for the elimination of sensitiveness to initial solutions or requirements for admissible load intervals. The paper is illustrated with results of several benchmark problems with simulated measurement data and various numbers of unknown load parameters. The results comparison, between standard element-free methods with selected optimization algorithms as well as the proposed Monte Carlo solution approach is presented and is especially focused on CPU times. [ABSTRACT FROM AUTHOR]

This paper considers the dynamic output feedback robust model predictive control (MPC) for a system with both polytopic model parametric uncertainty and bounded disturbance. For this topic, the techniques for handling the unknown true state are crucial, and the strict guarantee of the input/output/state constraints requires replacing the true state by its bounds in the optimisation problems. Previously, in the separate works, we (i) gave the general polyhedral bound; (ii) proposed the general ellipsoidal bound; (iii) applied some special polyhedral bounds to tighten the ellipsoidal bound since the latter is crucial for guaranteeing recursive feasibility. In this paper, (i)-(iii) are unified, and the up-to-date least conservative treatment of the true state bound is given, so the control performance can be greatly improved. The contribution mainly lies in overcoming the difficulties in developing technical details for the unification. A numerical example is given to illustrate the effectiveness of the new method. [ABSTRACT FROM AUTHOR]

In this paper, based on the 3-1 piecewise nonlinear complementarity problem (NCP) function, we proposed a smoothing Newton-type method for the generalized nonlinear complementarity problem (GNCP) with a modified non-monotone line search. The algorithm for a GNCP is more difficult than that for an NCP, because two functions must be considered in the problem. We reformulate the (GNCP) to a smoothing system of equations by two independent variables, and then develop a smoothing Newton-type method for solving it. Under reasonable conditions, we obtain the global convergent properties. Also, the numerical experiments are reported in this paper. [ABSTRACT FROM AUTHOR]

This paper considers the estimation of parameters of AR(p) models for time series witht-distribution via EM-based algorithms. The paper develops asymptotic properties for the estimation to show that the estimators are efficient. Also testing theory for the estimators is considered. The robustness of the estimators and various tests to deviations from an assumed model is investigated. The study shows that the algorithms have equal estimation efficiency even if the error distribution is miss-specified or perturbed by outliers. Interestingly, the estimators from these algorithms performed better than that of the Modified Maximum Likelihood (MML) considered in Tiku et al. (2000). [ABSTRACT FROM AUTHOR]

H-matrices play an important role in applied sciences such as numerical analysis and optimization theory. An attractive question is to identify whether a given matrix is an H-matrix. In this paper, we propose a new iterative algorithm for identifying H-matrices. We show that the proposed algorithm has linear convergence and can determine the H-matrix characterization for any given matrix. Its performance is illustrated in a set of numerical tests. [ABSTRACT FROM AUTHOR]

The pavement maintenance and rehabilitation (M&R) strategy selection problem is an exceedingly hard problem to solve optimally. In this paper, a novel Adaptive Hybrid Genetic Algorithm (AHGA) is proposed which incorporates Local Search (LS) techniques into Genetic Algorithms (GA) to improve the overall efficiency and effectiveness of the search. Specifically, it contains two dynamic learning mechanisms to guide and combine the exploration and exploitation search processes adaptively. The first learning mechanism aims to assess the worthiness of conducting an LS reactively and to control the computational resources allocated to the application of this search technique efficiently. The second learning mechanism uses instantaneously learned probabilities to select from a set of pre-defined LS operators which compete against each other for selection which is the most appropriate at any particular stage of the search to take over from the evolutionary-based search process. The new AHGA is compared to a non-hybridized version of the GA by applying the algorithms to several case studies in order to determine the best pavement M&R strategy that minimizes the present value of the total M&R costs. The results show that the proposed AHGA statistically outperforms the traditional GA in terms of efficiency. [ABSTRACT FROM AUTHOR]

The paper presents a model for a system exposed to a random environment characterized by the Poisson shock processes. A subset of the system components ℜM is required for a mission completion. Failures of some components of this subset terminate a mission, whereas failures of other components are not terminal and allow for a rescue operation that is activated immediately upon failure. This operation is performed by a subset ℜR of the system components and succeeds if all components from ℜR survive all shocks occurring until its completion. The subsets ℜM and ℜR overlap. The duration of the rescue operation depends on the time of its activation. The components that are engaged only in the rescue operation remain in the warm standby mode during the primary mission. An approach for obtaining the mission success and the system survival probabilities is developed and an algorithm for the corresponding numerical computation is presented. An example analyzing the tradeoff between these two probabilities and illustrating optimization of the system protection design is given. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of minimizing the expected finite-horizon cost for piecewise deterministic Markov decision processes. The transition rates may be unbounded, and the cost functions are allowed to be unbounded from above and from below. The optimality is over the general history-dependent policies, where the control is continuously acting in time. The infinitesimal approach is employed to establish the associated Hamilton-Jacobi-Bellman equation, via which the existence of optimal policies is proved. An example is provided to verify all the assumptions proposed. [ABSTRACT FROM AUTHOR]

This paper presents a multi-objective optimization methodology that applies the Non-dominated Sorting Genetic Algorithm-II(NSGA-II) to propeller design, and realizes Fluid-Structure Interaction (FSI) weak-coupling based on Panel Method (PM) and the Finite Element Method (FEM). The FSI iterative process and the convergent pressure coefficient distribution and pressure fluctuation of HSP (a propeller installed on a Japanese bulk freighter - Seiun-Maru) are numerical calculated. The FSI results turn out to have higher precision than those without FSI. The appropriate optimization parameters are chosen after studying five cases. The Sobol method, a global Sensitivity Analysis (SA) algorithm, is used to quantify the dependence of objectives and constraints on the input parameters. In the multi-objective optimization methodology, efficiency, unsteady force, and mass are chosen as optimum objectives under certain constraints. Effectiveness and robustness of the methodology are validated by running the program starting from four different random values, which all improve the objectives and converge to the similar results. The proposed multi-objective optimization methodology could be a promising tool for propeller design to help improve design efficiency and ability in the future. [ABSTRACT FROM AUTHOR]

In this paper we study the stability of the minimal solutions of set optimization problems. We provide sufficient conditions for the upper and lower semicontinuity and compactness of the minimal solutions of parametric set optimization problems whose objective values are not necessarily compact. [ABSTRACT FROM AUTHOR]

In this paper, we present two penalty-splitting inspired iteration schemes (PFFSA) and (PFFSA) for hierarchical equilibrium problems in Hilbert space. Based on the Opial-Passty lemma, we propose weak ergodic convergence and weak convergence of the iterative sequences generated by the Forward-Forward algorithm (PFFSA) and the Forward-Backward algorithm (PFFSA), which are proved under quite mild conditions: the bifunction of the two level equilibrium problems are supposed pseudomonotone. For strong convergence, we first add a strong monotonicity condition on the objective bifunction. We present after, a strong convergence result of algorithm (PFFSA) by adding a topological assumption, i.e. the objective bifunction is of class . Some examples are given to illustrate our results. The first example deals with pseudomonotone variational inequalities and convex minimization problem in the upper level problem. In the second one, we propose a convex minimization in the lower-level problem, where strong convergence of (PFFSA) to a minimum point is insured under infcompactness condition for objective function. These convergence results are new and generalize some recent results in this field. [ABSTRACT FROM AUTHOR]

In this paper, we propose a large-update primal-dual interior-point algorithm for linear optimization problems based on a new kernel function with a trigonometric growth term. By simple analysis, we prove that in the large neighbourhood of the central path, the worst case iteration complexity of the new algorithm is bounded above by , which matches the currently best known iteration bound for large-update methods. Moreover, we show that, most of the so far proposed kernel functions can be rewritten as a kernel function with trigonometric growth term. Finally, numerical experiments on some test problems confirm that the new kernel function is well promising in practice in comparison with some existing kernel functions in the literature. [ABSTRACT FROM AUTHOR]

The first aim of this paper is to introduce a modular test for the three-way contingency table (TT). The second aim is to describe the procedure of generating TT using the bar method. The third aim is on the one hand to suggest the measure of untruthfulness of H0 and on the other hand to compare the quality of independence tests by using their power. Critical values for analyzed statistics were determined by simulating the Monte Carlo method. [ABSTRACT FROM AUTHOR]

This paper proposes an affine scaling interior trust-region method in association with nonmonotone line search filter technique for solving nonlinear optimization problems subject to linear inequality constraints. Based on a Newton step which is derived from the complementarity conditions of linear inequality constrained optimization, a trust-region subproblem subject only to an ellipsoidal constraint is defined by minimizing a quadratic model with an appropriate quadratic function and scaling matrix. The nonmonotone schemes combining with trust-region strategy and line search filter technique can bring about speeding up the convergence progress in the case of high nonlinear. A new backtracking relevance condition is given which assures global convergence without using the switching condition used in the traditional line search filter technique. The fast local convergence rate of the proposed algorithm is achieved which is not depending on any external restoration procedure. The preliminary numerical experiments are reported to show effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, based on a new smoothing function, the general box constrained variational inequalities are solved by a smoothing Newton algorithm with a nonmonotone line search. The proposed algorithm is proved to be globally and locally superlinearly convergent under suitable assumptions. The preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

In the paper, we consider the bioprocess system optimal control problem. Generally speaking, it is very difficult to solve this problem analytically. To obtain the numerical solution, the problem is transformed into a parameter optimization problem with some variable bounds, which can be efficiently solved using any conventional optimization algorithms, e.g. the improved Broyden-Fletcher-Goldfarb-Shanno algorithm. However, in spite of the improved Broyden-Fletcher-Goldfarb-Shanno algorithm is very efficient for local search, the solution obtained is usually a local extremum for non-convex optimal control problems. In order to escape from the local extremum, we develop a novel stochastic search method. By performing a large amount of numerical experiments, we find that the novel stochastic search method is excellent in exploration, while bad in exploitation. In order to improve the exploitation, we propose a hybrid numerical optimization algorithm to solve the problem based on the novel stochastic search method and the improved Broyden-Fletcher-Goldfarb-Shanno algorithm. Convergence results indicate that any global optimal solution of the approximate problem is also a global optimal solution of the original problem. Finally, two bioprocess system optimal control problems illustrate that the hybrid numerical optimization algorithm proposed by us is low time-consuming and obtains a better cost function value than the existing approaches. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonsmooth vector optimization problem involving locally Lipschitz generalized approximate convex functions and find some relations between approximate convexity and generalized approximate convexity. We establish relationships between vector variational inequalities and nonsmooth vector optimization problem using the generalized approximate convexity as a tool. [ABSTRACT FROM AUTHOR]

In this paper, we propose an arc-search infeasible-interior-point method based on the wide neighbourhoodfor linear complementarity problems over symmetric cones with the Cartesian-property (-SCLCP). The algorithm searches the optimizers along the ellipses that approximate the central path. Moreover, we derive the complexity bound of the algorithm which coincides with the currently best known theoretical complexity bounds for the short step path-following algorithm. Some numerical results are provided to demonstrate the computational performance of the proposed algorithm. [ABSTRACT FROM PUBLISHER]

This paper presents the numerical results of a shape optimisation problem with regard to delaying the transition of a Navier-Stokes flow field from laminar to turbulent by using the theory developed by Nakazawa and Azegami. The theory was reviewed within the framework of functional analysis and updated with another expression of the shape derivative with respect to the objective function. A computer program was developed with the FreeFEM++. Numerical analyses were performed for two types of problems: a two-dimensional Poiseuille flow field with a sudden expansion and a two-dimensional uniform flow field around an isolated body. From the first example, two local minimum points of symmetric and asymmetric flow fields were determined, and the asymmetric flow field was found to be more stable. With regard to the second example, we reached the local minimum point of an elliptical shape, and infrequently determined a solution converging to an elliptical shape with the bluff in the leeward direction. By comparison, the superiority of the elliptical shape was obvious. [ABSTRACT FROM AUTHOR]

Degradation analysis is a useful technique when life tests result in few or even no failures. The degradation measurements are recorded over time and the estimation of time-to-failure distribution plays a vital role in degradation analysis. The parametric method to estimate the time-to-failure distribution assumed a specific parametric model with known shape for the random effects parameter. To avoid any assumption about the model shape, a nonparametric method can be used. In this paper, we suggest to use the nonparametric fourth-order kernel method to estimate the time-to-failure distribution and its percentiles for the simple linear degradation model. The performances of the proposed method are investigated and compared with the classical kernel; maximum likelihood and ordinary least squares methods via simulation technique. The numerical results show the good performance of the fourth-order kernel method and demonstrate its superiority over the parametric method when there is no information about the shape of the random effect parameter distribution. [ABSTRACT FROM AUTHOR]

This paper introduces a Markov model in Phase II profile monitoring with autocorrelated binary response variable. In the proposed approach, a logistic regression model is extended to describe the within-profile autocorrelation. The likelihood function is constructed and then a particle swarm optimization algorithm (PSO) is tuned and utilized to estimate the model parameters. Furthermore, two control charts are extended in which the covariance matrix is derived based on the Fisher information matrix. Simulation studies are conducted to evaluate the detecting capability of the proposed control charts. A numerical example is also given to illustrate the application of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we propose an iteratively reweightedminimization algorithm (IRL1 algorithm) for solving the elasticminimization problem. We prove that any sequence generated by the IRL1 algorithm is bounded and asymptotically regular. We also prove that the sequence is convergent for any rationaland the limit is a stationary point of the elasticminimization problem. Moreover, under certain conditions, we present an error bound between the limit point of convergent sequence and the sparse solution of underdetermined linear system. Numerical experiments on sparse vector recovery are presented to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the synchronisation problems of multi-agent systems with asynchronous and synchronous event-triggered control under a novel event-triggered condition are solved. Our event-triggered control protocols only require each agent to send its state information to its neighbouring agents when an event-triggered condition is satisfied. Such control protocols substantially reduce the cost of communication. It is worth mentioning that the proposed protocols also ensure that the synchronisation of the multi-agent system with asynchronous and synchronous event-triggered can be achieved asymptotically without Zeno-behaviour. Meanwhile, an ultimate synchronisation trajectory is given. Moreover, our results are applied to solve the formation control problem. Some numerical simulations are presented to illustrate the effectiveness of our protocols. [ABSTRACT FROM AUTHOR]

This paper deals with an optimal control problem of Bolza type for a class of parabolic equations. It consists in finding the initial datum that minimizes a cost functional, which comprises an energy term on the control and a regulation term given by a distributed cost on the state, and such that the final state lies within a prescribed distance to a given target. Beyond the particularities of the chosen problem, our aim here is to propose a new methodologybased on a spectral decomposition of the operator governing the evolution of the system, describe its implementation for this kind of problem, and finally perform some preliminary numerical experiments to assess its behaviour. [ABSTRACT FROM AUTHOR]

In this paper, we solve an optimal control problem for a class of time-invariant switched stochastic systems with multi-switching times, where the objective is to minimise a cost functional with different costs defined on the states. In particular, we focus on problems in which a pre-specified sequence of active subsystems is given and the switching times are the only control variables. Based on the calculus of variation,we derive the gradient of the cost functional with respect to the switching times on an especially simple form, which can be directly used in gradient descent algorithms to locate the optimal switching instants. Finally, a numerical example is given, highlighting the validity of the proposed methodology. [ABSTRACT FROM AUTHOR]

In this paper, a novel sliding-mode analysis method is proposed for the traditional sliding-mode-based extremum seeking control (ESC) scheme. Based on the method, a more rigorous and more concise stability proof of the scheme is presented. Furthermore, a novel switching-based ESC scheme is designed by combining traditional sliding-mode-based ESC and a perturbation-based ESC without steady-state oscillation. This proposed scheme can overcome the steady-state oscillation of sliding-mode-based ESC scheme as well as keep rapid, robust convergence. The stability analysis of the proposed scheme is also provided. The simulation examples show the effectiveness and advantages of the scheme. [ABSTRACT FROM AUTHOR]

This paper studies the distributed consensus problem in sampled-data multi-agent systems with directed network topologies subject to a quantisation constraint. Different from the widely used consensus protocol which exploits current information, we adopt a distributed proportional-differential (PD)-like protocol. First, we provide a necessary and sufficient condition of control gains which guarantee the consensus with the assumption that real-valued communication information can be obtained. Next, we analyse the quantisation effects in system performances under the proposed protocol; it is proved that the quantised consensus can be achieved. Finally, by providing numerical examples, we show that with appropriate parameters, the consensus can be achieved and the quantisation noises can be attenuated effectively. [ABSTRACT FROM AUTHOR]

Modern marine dynamic positioning (DP) systems are commonly constructed on the basis of nonlinear asymptotic observers. The primary reason for the observer's employment is to restore deficient information concerning the unmeasured velocities of the vessel. Nevertheless, using a number of separate items in addition to the observers, it is also possible to achieve desirable dynamical features of the closed-loop connection. The paper is devoted to the problem of synthesis of these items for marine vessels, which are controlled by DP systems under the action of sea wave disturbances. The essence of the problem is to identify a transfer matrix of the adjustable corrective item (filter), minimising the intensity of the control action determined by high-frequency sea wave components. The correspondent dynamic of a closed-loop system realises an economical regime of vessel motion with the aim to reduce general fuel consumption and to prevent the wearing down of actuators. A specialised approach for designing the filters is proposed that provides asymptotic stability and the integral action of a control. Applicability and effectiveness of this approach are illustrated by the practical example of DP system synthesis. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a bi-level-based optimization model and develop a genetic algorithms (GA)-based method to solve the optimal toll design with elastic demand problem for congestion management and to determine the second-best linked-based optimal toll locations and toll levels simultaneously. The upper-level subprogram is to maximize the total social welfare given certain toll level constraints. The lower level subprogram is a traditional user equilibrium problem with elastic demand. The proposed GA model is applied to the Sioux Falls network, which has 76 links and 24 OD-pairs, assuming homogeneous users. Comprehensive numerical results including solutions achieved under continuous tolling and discrete tolling schemes, tolling on optimized links and tolling on heuristically selected most congested links are carefully presented and compared. The impact of value of time and the elastic demand sensitivity are also comprehensively investigated. [ABSTRACT FROM PUBLISHER]

The (multistep) one-shot method for design optimization problems has been successfully implemented for various applications. To this end, a slowly convergent primal fixed-point iteration of the state equation is augmented by an adjoint iteration and a corresponding preconditioned design update. In this paper we present a modification of the method that allows for additional equality constraints besides the usual state equation. A retardation analysis and the local convergence of the method in terms of necessary and sufficient conditions are given, which depend on key characteristics of the underlying problem and the quality of the utilized preconditioner. [ABSTRACT FROM PUBLISHER]

Continuous flow intersection (CFI) is a potential treatment to relieve traffic congestion at intersections. Conventional geometric design and signal timing of CFI are usually performed in a trial-and-error way, which may not always yield the truly optimal design. In this paper, an integrated optimization model for design of lane markings, the distances between the crossovers and the main intersection, and signal timings are proposed for the full CFI. The optimization problem is formulated as a mixed-integer non-linear programming problem, which is further transformed into a series of mixed-integer linear programming models and solved by the standard branch-and-bound technique. Numerical analysis results further validate the effectiveness and applicability of the proposed model. [ABSTRACT FROM PUBLISHER]

This paper specifies a dispatching decision support system devoted to managing intermodal logistics operations while countering delay and delay propagation. When service disruptions occur within a logistics network where schedule coordination is employed, a dispatching control model determines through an optimization process whether each ready outbound vehicle should be dispatched immediately or held to wait for some late incoming vehicles. Decisions should consider potential missed-connection costs that may occur not only at the next transfer terminals but also at hubs located further downstream. Numerical examples and a sensitivity analysis with different slack time settings for attenuating delay propagation are presented. [ABSTRACT FROM AUTHOR]

In this paper, a finite filter is used in the structure of the Barzilai–Browein (BB) gradient method in order to propose a new modified BB algorithm for solving large-scale unconstrained optimization problems. Our algorithm is equipped with a relaxed nonmonotone line search technique which allows the algorithm to enjoy the nonmonotonicity properties from scratch. Under some suitable conditions, the global convergence property of the new proposed algorithm is established. Numerical results on some test problems in CUTEr library show the efficiency and effectiveness of the new algorithm in practice too. [ABSTRACT FROM PUBLISHER]

In this paper, existence of critical point and weak efficient point of vector optimization problem is studied. A sequence of points in n-dimension is generated using positive definite matrices like Quasi-Newton method. It is proved that accumulation points of this sequence are critical points or weak efficient points under different conditions. An algorithm is provided in this context. This method is free from any kind of priori chosen weighting factors or any other form of a priori ranking or ordering information for objective functions. Also, this method does not depend upon initial point. The algorithm is verified in numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new numerical technique which we call fractional Chebyshev finite difference method. The algorithm is based on a combination of the useful properties of Chebyshev polynomial approximation and finite difference method. We implement this technique to solve numerically the non-linear programming problem which are governed by fractional differential equations (FDEs). The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the Caputo fractional derivatives. This operational matrix method can be regarded as a non-uniform finite difference scheme. The error bound for the fractional derivatives is introduced. The application of the method to the generated FDEs leads to algebraic systems which can be solved by an appropriate method. Two numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method. A comparison with the fourth-order Runge–Kutta method is given. [ABSTRACT FROM PUBLISHER]

In this paper, a modified Liu–Storey conjugate gradient method is proposed. The method can generate sufficient descent directions for non-linear unconstrained optimization problems. A global convergence result is established when the line search fulfils the strong Wolfe conditions. Moreover, the-linear convergence rate of the methods is proved. The extensive numerical results show that the proposed method is efficient for the unconstrained optimization problems in the CUTEr library. [ABSTRACT FROM AUTHOR]

In this paper we propose an augmented Lagrangian trust region method for equality constrained optimization. Different from standard augmented Lagrangian methods which minimize the augmented Lagrangian function for fixed Lagrange multiplier and penalty parameter at each iteration, the proposed method tries to minimize its second-order approximation function. We propose a new strategy for adjusting the penalty parameter. With adaptive update of Lagrange multipliers, we prove the global convergence of the proposed method. Numerical results on test problems from the CUTEr collection are also reported. [ABSTRACT FROM PUBLISHER]

In this paper, an alternative optimization strategy incorporating the ideas of lexicographic optimization and evolutionary algorithms is presented. The given optimization problem is approximated by others in which priorities are given. Under the sequential optimization method, they are optimized, not exhaustively, in order to produce an initial point for the given problem. An important role in the proposed approach plays the way of generating the involved problems and the given priorities on them. General principles to produce the objective functions of the involved problems are proposed. An algorithm named LexOpt Algorithm, which implements the suggested process, is given. Numerical results via LexOpt Algorithm, on a set of widely used test problems show noticeable promising convergence behaviour of the proposed strategy in comparison with the utilized optimization methods. [ABSTRACT FROM AUTHOR]

This paper suggests a weighting proposal forknearest neighbours (kNN) classifier, which uses the Artificial Bee Colony (ABC) algorithm. The proposed approach is named as ABC-based distance-weightedkNN (dW-ABCkNN). The main idea of the hybrid algorithm is to assign random weights over sorted distances ofkNN and to find the optimal weights, which achieve better classification performance. ABC algorithm carries out the weight determination operation. To evaluate the results, the data-sets from UCI machine learning repository are used. The classification performance of the dW-ABCkNN is compared with distance-weightedkNN (dW-kNN) and equally weightedkNN (eW-kNN) algorithms. The numerical simulations show that dW-ABCkNN always outperforms eW-kNN approach. It improves the correct classification performance of dWkNN in most data-sets, especially at small values ofk. Experimental results confirm the merit of dW-ABCkNN approach. [ABSTRACT FROM AUTHOR]

Preconditioning techniques are important in solving linear problems, as they improve their computational properties. Scaling is the most widely used preconditioning technique in linear optimization algorithms and is used to reduce the condition number of the constraint matrix, to improve the numerical behavior of the algorithms and to reduce the number of iterations required to solve linear problems. Graphical processing units (GPUs) have gained a lot of popularity in the recent years and have been applied for the solution of linear optimization problems. In this paper, we review and implement ten scaling techniques with a focus on the parallel implementation of them on GPUs. All these techniques have been implemented under the MATLAB and CUDA environment. Finally, a computational study on the Netlib set is presented to establish the practical value of GPU-based implementations. On average the speedup gained from the GPU implementations of all scaling methods is about 7×. [ABSTRACT FROM PUBLISHER]

In this paper, an algorithm is proposed for solving a class of nonconvex fractional problems that result from the optimal correction of inconsistent linear equality systems. The main difficulty with this problem is its nonconvexity. Nevertheless, we can show that a global optimal solution to this problem can be found by solving a very simple univariate equation on a closed interval. Computing a value and a subgradient of the function in the equation consists of solving a single trust region subproblem. This function is convex and strictly increasing. As a result, we provide an alternative algorithm based on generalized Newton's direction. Numerical examples are given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]