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The paper proposes a new extragradient algorithm for solving strongly pseudomonotone equilibrium problems which satisfy a Lipschitz-type condition recently introduced by Mastroeni in auxiliary problem principle. The main novelty of the paper is that the algorithm generates the strongly convergent sequences in Hilbert spaces without the prior knowledge of Lipschitz-type constants and any hybrid method. Several numerical experiments on a test problem are also presented to illustrate the convergence of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we present an interior point method for nonlinear programming that avoids the use of penalty function or filter. We use an adaptively perturbed primal dual interior point framework to computer trial steps and a central path technique is used to keep the iterate bounded away from 0 and not to deviate too much from the central path. A trust-funnel-like strategy is adopted to drive convergence. We also use second-order correction (SOC) steps to achieve fast local convergence by avoiding Maratos effect. Furthermore, the presented algorithm can avoid the blocking effect. It also does not suffer the blocking of productive steps that other trust-funnel-like algorithm may suffer. We show that, under second-order sufficient conditions and strict complementarity, the full Newton step (combined with an SOC step) will be accepted by the algorithm near the solution, and hence the algorithm is superlinearly local convergent. Numerical experiments results, which are encouraging, are reported. [ABSTRACT FROM AUTHOR]

Our underlying motivation is the iterative method for the implementation of the limit representation of the Moore-Penrose inverse lim αI0 (αI + A*A)-1 A* from [Žukovski, Lipcer, On recurent computation of normal solutions of linear algebraic equations, Ž. Vicisl. Mat. i Mat. Fiz. 12 (1972), 843-857] and [Žukovski, Lipcer, On computation pseudoinverse matrices, Ž. Vicisl. Mat. i Mat. Fiz. 15 (1975), 489-492]. The iterative process for the implementation of the general limit formula lim αI0 (αI + R*S)-1R* was defined in [P.S. Stanimirović, Limit representations of gen- eralized inverses and related methods, Appl. Math. Comput. 103 (1999), 51-68]. In this paper we develop an improvement of this iterative process. The iterative method defined in such a way is able to produce the result in a predefined number of iterative steps. Convergence properties of defined iterations are further investigated. [ABSTRACT FROM AUTHOR]

In this paper, we consider an elliptic equation with strongly varying coefficients. Interest in the study of these equations is connected with the fact that this type of equation is obtained when using the fictitious domain method. In this paper, we propose a special method for the numerical solution of elliptic equations with strongly varying coefficients. A theorem is proved for the rate of convergence of the iterative process developed. A computational algorithm and numerical calculations are developed to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In the Artificial Bee Colony (ABC) algorithm, the employed bee and the onlooker bee phase involve updating the candidate solutions by changing a value in one dimension, dubbed one-dimension update process. For some problems which the number of dimensions is very high, the one-dimension update process can cause the solution quality and convergence speed drop. This paper proposes a new algorithm, using reinforcement learning for solution updating in ABC algorithm, called R-ABC. After updating a solution by an employed bee, the new solution results in positive or negative reinforcement applied to the solution dimensions in the onlooker bee phase. Positive reinforcement is given when the candidate solution from the employed bee phase provides a better fitness value. The more often a dimension provides a better fitness value when changed, the higher the value of update becomes in the onlooker bee phase. Conversely, negative reinforcement is given when the candidate solution does not provide a better fitness value. The performance of the proposed algorithm is assessed on eight basic numerical benchmark functions in four categories with 100, 500, 700, and 900 dimensions, seven CEC2005’s shifted functions with 100, 500, 700, and 900 dimensions, and six CEC2014’s hybrid functions with 100 dimensions. The results show that the proposed algorithm provides solutions which are significantly better than all other algorithms for all tested dimensions on basic benchmark functions. The number of solutions provided by the R-ABC algorithm which are significantly better than those of other algorithms increases when the number of dimensions increases on the CEC2005’s shifted functions. The R-ABC algorithm is at least comparable to the state-of-the-art ABC variants on the CEC2014’s hybrid functions. [ABSTRACT FROM AUTHOR]

In this paper, we present a method for portfolio selection based on the consideration on deformed exponentials in order to generalize the methods based on the gaussianity of the returns in portfolio, such as the Markowitz model. The proposed method generalizes the idea of optimizing mean-variance and mean-divergence models and allows a more accurate behavior for situations where heavy-tails distributions are necessary to describe the returns in a given time instant, such as those observed in economic crises. Numerical results show the proposed method outperforms the Markowitz portfolio for the cumulated returns with a good convergence rate of the weights for the assets which are searched by means of a natural gradient algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a primal method for finding the minimum L-infinity solution to under-determined linear systems of equations. The method is a two-phase method. Line search is performed at both phases. We establish a condition for a direction to be descent. The convergence proof of the method is shown. Expedient numerical schemes can be used whenever appropriate. Results are presented, which show the superiority of the method over some well-known methods. [ABSTRACT FROM AUTHOR]

Threshold dynamics and its extensions have proven useful in computing interfacial motions in applications as diverse as materials science and machine learning. Certain desirable properties of the algorithm, such as unconditional monotonicity in two-phase ows and gradient stability more generally, hinge on positivity properties of the convolution kernel and its Fourier transform. Recent developments in the analysis of this class of algorithms indicate that sometimes, as in the case of certain anisotropic curvature ows arising in materials science, these properties of the convolution kernel cannot be expected. Other applications, such as machine learning, would benefit from as great a level of exibility in choosing the convolution kernel as possible. In this paper, we establish certain desirable properties of threshold dynamics, such as gamma convergence of its associated energy, for a substantially wider class of kernels than has been hitherto possible. We also present variants of the algorithm that extend some of these properties to even wider classes of convolution kernels. [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 we discuss different definitions of variable-order derivatives of high order and we propose accurate and robust algorithms for their approximate calculation. The proposed algorithms are based on finite difference approximations and B-spline interpolation. We compare the performance of the algorithms by experimental convergence order. Numerical examples are presented demonstrating the efficiency and accuracy of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Solving feasibility problems is a central task in mathematics and the applied sciences. One particularly successful method is the Douglas--Rachford algorithm. In this paper, we provide many new conditions sufficient for finite convergence. Numerou s examples illustrate our results. [ABSTRACT FROM AUTHOR]

In the paper, we introduce a class of delay differential variational inequalities consisting of a system of delay differential equations and variational inequalities. The existence conclusion of Carathéodory's weak solution for delay differential variational equalities is obtained. Furthermore, an algorithm for solving the delay differential variational inequality is shown, and the convergence analysis for the algorithm is given. Finally, a numerical example is given to verify the validity of the algorithm. [ABSTRACT FROM AUTHOR]

Matsumoto, Saito and Matoba recently proposed the Walsh figure of merit (WAFOM), which is a computable criterion for quasi-Monte Carlo point sets using digital nets. Several algorithms have been proposed for finding low-WAFOM point sets. In the existing algorithms, the number of points is fixed in advance, but extensible point sets are preferred in some applications. In this paper, we propose a random search algorithm for extensible low-WAFOM point sets. For this, we introduce a method that uses lookup tables to compute WAFOM faster. Numerical results show that our extensible low-WAFOM point sets are comparable with Niederreiter-Xing sequences for some low-dimensional and smooth test functions. [ABSTRACT FROM AUTHOR]

In this paper, the Hager and Zhang (HZ) conjugate gradient (CG) method and the modified HZ (MHZ) CG method are presented for large-scale nonsmooth convex minimization. Under some mild conditions, convergent results of the proposed methods are established. Numerical results show that the presented methods can be better efficiency for large-scale nonsmooth problems, and several problems are tested (with the maximum dimensions to 100,000 variables). [ABSTRACT FROM AUTHOR]

Time–frequency analysis for non-linear and non-stationary signals is extraordinarily challenging. To capture features in these signals, it is necessary for the analysis methods to be local, adaptive and stable. In recent years, decomposition based analysis methods, such as the empirical mode decomposition (EMD) technique pioneered by Huang et al., were developed by different research groups. These methods decompose a signal into a finite number of components on which the time–frequency analysis can be applied more effectively. In this paper we consider the Iterative Filtering (IF) approach as an alternative to EMD. We provide sufficient conditions on the filters that ensure the convergence of IF applied to any L 2 signal. Then we propose a new technique, the Adaptive Local Iterative Filtering (ALIF) method, which uses the IF strategy together with an adaptive and data driven filter length selection to achieve the decomposition. Furthermore we design smooth filters with compact support from solutions of Fokker–Planck equations (FP filters) that can be used within both IF and ALIF methods. These filters fulfill the derived sufficient conditions for the convergence of the IF algorithm. Numerical examples are given to demonstrate the performance and stability of IF and ALIF techniques with FP filters. In addition, in order to have a complete and truly local analysis toolbox for non-linear and non-stationary signals, we propose new definitions for the instantaneous frequency and phase which depend exclusively on local properties of a signal. [ABSTRACT FROM AUTHOR]

In this paper, we revisit the augmented Lagrangian method for a class of nonsmooth convex optimization. We present the Lagrange optimality system of the augmented Lagrangian associated with the problems, and establish its connections with the standard optimality condition and the saddle point condition of the augmented Lagrangian, which provides a powerful tool for developing numerical algorithms: we derive a Lagrange–Newton algorithm for the nonsmooth convex optimization, and establish the nonsingularity of the Newton system and the local convergence of the algorithm. [ABSTRACT FROM PUBLISHER]

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 we study numerical stability of path-based algorithms for the traffic assignment problem. These algorithms are based on decomposition of the original problem into smaller sub-problems which are optimized sequentially. Previously, path-based algorithms were numerically tested only in the setting of moderate requirements to the level of solution precision. In this study we analyse convergence of these methods when the convergence measure approaches machine epsilon of IEEE double precision format. In particular, we demonstrate that the straightforward implementation of one of the algorithms of this group (projected gradient) suffers from loss of precision and is not able to converge to highly precise solution. We propose a way to solve this problem and test the proposed adjusted version of the algorithm on various benchmark instances. [ABSTRACT FROM AUTHOR]

A trust-region algorithm in association with line search filter technique for solving nonlinear equality constrained programming is proposed in this paper. In the current iteration, the trial step providing sufficient descent is generated by solving a corresponding trust-region subproblem. Then, the step size is decided by backtracking line search together with filter technique to obtain the next iteration point. The advantage of this method is that resolving trust-region subproblem many times to determine a new iteration point in traditional trust-region method can be avoided and hence the expensive computation can be lessened. And the difficult decisions in regard to the choice of penalty parameters in the merit functions can be avoided by using filter technique. Second order correction steps are introduced in the proposed algorithm to overcome Maratos effect. Convergence analysis shows that fast local convergence can be achieved under some mild assumptions. The preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

In this paper a nonlinear backward parabolic problem in one dimensional space is considered. Using a suitable iterative algorithm, the problem is converted to a linear backward parabolic problem. For the corresponding problem, the backward finite differences method with suitable grid size is applied. It is shown that if the coefficients satisfy some special conditions, this algorithm not only is convergent, but also is conditionally stable. Moreover, it is proved that the estimated values converge to the exact solution of the problem. All these approaches examined in some numerical examples. corresponding theorems for the convergency and stability of the solution are studied. [ABSTRACT FROM AUTHOR]

Vibro-acoustic analysis of a rail vehicle cabin is presented in this paper. Vehicle is modeled by an air cavity coupled to a flexible floor panel. Analytical procedure is employed to predict the structural-borne noise in the vehicle model generated by random excitation of the panel. In this study, natural frequencies of the coupled system are obtained and then the sound pressure field inside the cavity is analytically determined. In order to find dynamic responses of the coupled system in the time domain, Durbin's numerical Laplace transform inversion algorithm is employed. Convergence of the algorithm is verified and eventually a parametric study is carried out to investigate the effects of rail irregularity and vehicle speed on the time and frequency responses. [ABSTRACT FROM AUTHOR]

In the paper, first, we introduce a new hybrid projection algorithm and present its strong convergence theorem. Next, we analyze different hybrid algorithms in computing and conclude that our proposed algorithm has an advantage. Finally, the numerical experiments validate the efficiency and advantages of the new algorithm. [ABSTRACT FROM AUTHOR]

In the CQ-like algorithms for the split feasibility problem, in order to get the step-size, one has to compute the largest eigenvalue of the related matrix or use some line search scheme. Our contribution in this short note is to give a simple CQ-like algorithm in which the step-size is directly computed. The algorithm presented in this paper not only need not to compute the largest eigenvalue of the related matrix but also need not to use any line search scheme. The theoretical convergence and numerical results are also given. [ABSTRACT FROM AUTHOR]

Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity continues to grow because of their usefulness in data analysis, machine learning, and other areas of current interest. This paper describes the fundamentals of the coordinate descent approach, together with variants and extensions and their convergence properties, mostly with reference to convex objectives. We pay particular attention to a certain problem structure that arises frequently in machine learning applications, showing that efficient implementations of accelerated coordinate descent algorithms are possible for problems of this type. We also present some parallel variants and discuss their convergence properties under several models of parallel execution. [ABSTRACT FROM AUTHOR]

Trust region methods are a class of numerical methods for optimization. Unlike line search type methods where a line search is carried out in each iteration, trust region methods compute a trial step by solving a trust region subproblem where a model function is minimized within a trust region. Due to the trust region constraint, nonconvex models can be used in trust region subproblems, and trust region algorithms can be applied to nonconvex and ill-conditioned problems. Normally it is easier to establish the global convergence of a trust region algorithm than that of its line search counterpart. In the paper, we review recent results on trust region methods for unconstrained optimization, constrained optimization, nonlinear equations and nonlinear least squares, nonsmooth optimization and optimization without derivatives. Results on trust region subproblems and regularization methods are also discussed. [ABSTRACT FROM AUTHOR]

In this paper we deal with the numerical analysis of an adsorption dynamic model arising in a surfactant solution at the air–water interface; the diffusion model is considered together with the so-called Langmuir isotherm. An existence and uniqueness result is stated. Then, fully discrete approximations are introduced by using a finite element method and a hybrid combination of backward and forward Euler schemes. Error estimates are proved from which, under adequate additional regularity conditions, the linear convergence of the algorithm is derived assuming a dependence between both spatial and time discretization parameters. Finally, some numerical simulations are presented in order to demonstrate the accuracy of the algorithm and the behaviour of the solution for two commercially available surfactants. [ABSTRACT FROM AUTHOR]

In this paper we present a new trust-region SQP algorithm for nonlinear programming. This method avoids using a penalty function, nor a filter, and instead establishes a new step acceptance mechanism. Under some reasonable assumptions, the method can be proved to be globally convergent to a KT point. Preliminary numerical experiments are presented that show the potential efficiency of the new approach. [ABSTRACT FROM AUTHOR]

In this paper, we propose a generalized Laguerre spectral method for Fisher's-type equation with inhomogeneous boundary conditions on a semi-infinite interval. By reformulating the equation with suitable functional transform, it is shown that the generalized Laguerre approximations are convergent on a semi-infinite interval with spectral accuracy. An efficient and accurate algorithm based on the generalized Laguerre approximations to the transformed equation is developed and implemented. Numerical results show the efficiency of this approach and coincide well with theoretical analysis. [ABSTRACT FROM PUBLISHER]

In this paper, we introduce two iterative algorithms for finding common solutions of a finite family of variational inclusions for maximal monotone and inverse-strongly monotone mappings with the constraints of two problems: a generalized mixed equilibrium problem and a common fixed point problem of an infinite family of nonexpansive mappings and an asymptotically strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove some strong and weak convergence theorems for the proposed iterative algorithms under suitable conditions. [ABSTRACT FROM AUTHOR]

In the present paper, we propose several kinds of adaptively relaxed iterative algorithms with a new step size for solving the split feasibility problem in real Hilbert spaces. The proposed algorithms never terminate, while the known algorithms existing in the literature may terminate. Several weak and strong convergence theorems of the proposed algorithms have been established. Some numerical experiments are also included to illustrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

The multiple-sets split equality problem (MSSEP) requires finding a point x ∈∩Ni=1 Ci, y ∈∩Mj=1 Qj, such that Ax = By, where N and M are positive integers, {C1, C2,..., CN} and {Q1,Q2,...,QM} are closed convex subsets of Hilbert spaces H1, H2, respectively, and A : H1→H3, B : H2→H3 are two bounded linear operators. When N = M = 1, the MSSEP is called the split equality problem (SEP). If let B = I, then the MSSEP and SEP reduce to the well-known multiple-sets split feasibility problem (MSSFP) and split feasibility problem (SFP), respectively. Recently, some authors proposed many algorithms to solve the SEP and MSSEP. However, to implement these algorithms, one has to find the projection on the closed convex sets, which is not possible except in simple cases. One of the purposes of this paper is to study the SEP and MSSEP for a family of quasi-nonexpansive multi-valued mappings in the framework of infinite-dimensional Hilbert spaces, and propose an algorithm to solve the SEP and MSSEP without the need to compute the projection on the closed convex sets. [ABSTRACT FROM AUTHOR]

Abstract: In this paper a family of fixed point algorithms for the numerical resolution of some systems of nonlinear equations is designed and analyzed. The family introduced here generalizes the Petviashvili method and can be applied to the numerical generation of traveling waves in some nonlinear dispersive systems. Conditions for the local convergence are derived and numerical comparisons between different elements of the family are carried out. [Copyright &y& Elsevier]

In this paper, a two-level defect-correction Oseen iterative finite element method is presented for the stationary conduction–convection equations based on local Gauss integration. The method combines the defect-correction method, the two-level strategy, and the locally stabilized method. The stability and convergence of the proposed method are deduced. Finally, numerical examples verify the theoretical results of the proposed algorithm and show that it is highly efficient and reliable for the considered problem. [ABSTRACT FROM AUTHOR]

This paper extends the technique used in the damped BFGS method of Powell [Algorithms for nonlinear constraints that use Lagrange functions, Math. Program. 14 (1978), 224–248] to the Broyden family of quasi-Newton methods with applications to unconstrained optimization problems. Appropriate conditions on the damped technique are proposed to enforce safely the positive definiteness property for all Broyden's updates. It is shown that this technique maintains theq-superlinear convergence property of the restricted Broyden family of methods for uniformly convex functions. It also extends the global convergence property to all members of the family. Preliminary numerical results are described which show that appropriate ways for employing the proposed technique improve the performance of all members of the Broyden family of methods substantially and significantly in certain cases. They also enforce convergence of divergent quasi-Newton methods. [ABSTRACT FROM AUTHOR]

In this paper we analyse the Kaczmarz projection algorithm with remotest set control of projection indices. According to this procedure, at each iteration the projection index is one which gives the maximal absolute value of the corresponding residual. We prove that for under-determined full row rank systems and under some assumptions valid for problems arising in algebraic reconstruction of images in computerized tomography, this selection procedure has the property that each row index is selected at least once during the Kaczmarz algorithm iterations. [ABSTRACT FROM AUTHOR]

Co-simulation is a simulation technique for time dependent coupled problems in engineering that restricts the data exchange between subsystems to discrete communication points in time. In the present paper we follow the block-oriented framework in the recently established industrial interface standard FMI for Model Exchange and Co-Simulation v2.0 and study local and global error of co-simulation algorithms for systems with force-displacement coupling. A rather general convergence result for the co-simulation of coupled systems without algebraic loops shows zero-stability of co-simulation algorithms with force-displacement coupling and proves that order reduction of local errors does not affect the order of global errors. The theoretical investigations are illustrated by numerical tests in the novel FMI-compatible co-simulation environment SNiMoWrapper. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]