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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]

Multi objective programming problems have been widely applied to various engineering areas which include optimal design of an automotive engine, economics, and military strategies. In this paper, we propose a noninterior path following algorithm to solve a class of multi objective programming problems. Under suitable conditions, a smooth path will be proven to exist. This can give a constructive proof of the existence of solutions and lead to an implementable globally convergent algorithm. Several numerical examples are given to illustrate the results of this paper. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of a new class of nonconvex variational inequalities, named general regularized nonconvex variational inequalities. By using the auxiliary principle technique, a new modified predictor-corrector iterative algorithm for solving general regularized nonconvex variational inequalities is suggested and analyzed. The convergence of the iterative algorithm is established under the partially relaxed monotonicity assumption. As a consequence, the algorithm and results presented in the paper overcome incorrect algorithms and results existing in the literature. [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]

The purpose of this paper is to introduce and study a new class of nonlinear mixed family of random fuzzy and crisp operator equation couples in fuzzy normed spaces based on the random version of the theory of (φ, ψ)-contractor due to Mihet. Further, some new random iterative algorithms for solving this kind of nonlinear operator equation couples in fuzzy normed spaces are constructed and the convergence of iterative sequences generated by the algorithms under joint orbitally complete conditions is proved. As applications, some new common fixed point theorems for a mixed family of fuzzy and crisp operators in fuzzy normed spaces are also given. The results presented in this paper improve and generalize the corresponding results of recent works. [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]

Abstract: This paper proposes an algorithm for matrix minimum-distance projection, with respect to a metric induced from an inner product that is the sum of inner products of column vectors, onto the collection of all matrices with their rows restricted in closed convex sets. This algorithm produces a sequence of matrices by modifying a matrix row by row, over and over again. It is shown that the sequence is convergent, and it converges to the desired projection. The implementation of the algorithm for multivariate isotonic regressions and numerical examples are also presented in the paper. [Copyright &y& Elsevier]

A concave finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) is presented for scattering by a large body with nonuniform deep cavities. Different from the conventional FE-BI-MLFMA, the boundary integral equation in this concave FE-BI-MLFMA is established on a concave surface to reduce the region of the finite element method (FEM), which can significantly reduce the dispersion error from the FEM and improve the efficiency of FE-BI-MLFMA especially for nonuniform cavities. To eliminate the problem of slow convergence caused by concave surface, an efficient preconditioner based on the sparse approximate inverse (SAI) is constructed in this paper. Numerical performance of the constructed preconditioner based on the SAI is investigated in detail. Numerical experiments demonstrate the accuracy and efficiency of this SAI preconditioned concave FE-BI-MLFMA for nonuniform deep and large cavites. This SAI preconditioned concave FE-BI-MLFMA is parallelized to further improve its capability in this paper. An extremely big and deep nonuniform cavity has been calculated, demonstrating the great capability of this parallel concave FE-BI-MLFMA. [ABSTRACT FROM PUBLISHER]

Abstract: This paper concerns developing a numerical method of the Newton type to solve systems of nonlinear equations described by nonsmooth continuous functions. We propose and justify a new generalized Newton algorithm based on graphical derivatives, which have never been used to derive a Newton-type method for solving nonsmooth equations. Based on advanced techniques of variational analysis and generalized differentiation, we establish the well-posedness of the algorithm, its local superlinear convergence, and its global convergence of the Kantorovich type. Our convergence results hold with no semismoothness and Lipschitzian assumptions, which is illustrated by examples. The algorithm and main results obtained in the paper are compared with well-recognized semismooth and -differentiable versions of Newton’s method for nonsmooth Lipschitzian equations. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the filtering problem for polynomial systems. By means of Lyapunov theory and matrix inequality techniques, sufficient conditions are first obtained to ensure that the filtering error system is asymptotically stable and satisfies performance constraint. Then, a sufficient condition for the existence of desired filters is established with a free matrix introduced, which will greatly facilitate the design of filter matrices. By virtue of sum-of-squares (SOS) approaches, a convergent iterative algorithm is developed to tackle the polynomial  filtering problem. Note that the approach can be efficiently implemented by means of recently developed SOS decomposition techniques, and the filter matrices can be designed explicitly. Finally, a numerical example is given to illustrate the main results of this paper. [Copyright &y& Elsevier]

Abstract: The hybrid algorithm that combined particle swarm optimization with simulated annealing behavior (SA-PSO) is proposed in this paper. The SA-PSO algorithm takes both of the advantages of good solution quality in simulated annealing and fast searching ability in particle swarm optimization. As stochastic optimization algorithms are sensitive to their parameters, proper procedure for parameters selection is introduced in this paper to improve solution quality. To verify the usability and effectiveness of the proposed algorithm, simulations are performed using 20 different mathematical optimization functions with different dimensions. The comparative works have also been conducted among different algorithms under the criteria of quality of the solution, the efficiency of searching for the solution and the convergence characteristics. According to the results, the SA-PSO could have higher efficiency, better quality and faster convergence speed than compared algorithms. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a class of stochastic linear complementarity problems (SLCPs) with finitely many elements. We present a smoothing Newton algorithm for solving the SLCP. Under suitable conditions, we obtain the global convergence and locally quadratic convergence of the proposed algorithm. Some numerical results are reported in this paper, which confirm the good theoretical properties of the proposed algorithm. [Copyright &y& Elsevier]

In the paper [S.P. Rui and C.X. Xu, A smoothing inexact Newton method for nonlinear complementarity problems, J. Comput. Appl. Math. 233 (2010), pp. 2332–2338], the authors proposed an inexact smoothing Newton method for nonlinear complementarity problems (NCP) with the assumption that F is a uniform P function. In this paper, we present a non-monotone inexact regularized smoothing Newton method for solving the NCP which is based on Fischer–Burmeister smoothing function. We show that the proposed algorithm is globally convergent and has a locally superlinear convergence rate under the weaker condition that F is a P 0 function and the solution of NCP is non-empty and bounded. Numerical results are also reported for the test problems, which show the effectiveness of the proposed algorithm. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper, we try to solve the semidefinite program with box constraints. Since the traditional projection method for constrained optimization with box constraints is not suitable to the semidefinite constraints, we present a new algorithm based on the feasible direction method. In the paper, we discuss two cases: the objective function in semidefinite programming is linear and nonlinear, respectively. We establish the convergence of our algorithm, and report the numerical experiments which show the effectiveness of the algorithm. [Copyright &y& Elsevier]

This paper presents an adaptive method for tracking the amplitude, phase, and frequency of a time-varying sinusoid in white noise. Although the conventional techniques like adaptive linear elements and discrete or fast Fourier transforms are still widely used in many applications, their accuracy and convergence speed pose serious limitations under sudden supply frequency drift, fundamental amplitude, or phase variations. This paper, therefore, proposes a fast and low-complexity multiobjective Gauss–Newton algorithm for estimating the fundamental phasor and frequency of the power signal instantly and accurately. Further, the learning parameters in the proposed algorithm are tuned iteratively to provide faster convergence and better accuracy. The proposed method can also be extended to include time-varying harmonics and interharmonics mixed with noise of low signal-to-noise ratio with a great degree of accuracy. Numerical and experimental results are presented in support of the effectiveness of the new approach. [ABSTRACT FROM AUTHOR]

Abstract: Asian options are popular path-dependent financial derivatives. This paper uses lattices to price fixed-strike European-style Asian options that are discretely monitored. The algorithm proposed can also be applied to floating-strike Asian options as well because fixed-strike and floating-strike Asian options are related through an equation. The discretely monitored version is usually found in practice instead of the continuously monitored version usually encountered in the literature. This paper presents the first provably quadratic-time convergent lattice algorithm for pricing fixed-strike European-style discretely monitored Asian options. It is the most efficient lattice algorithm with convergence guarantees. The algorithm relies on the Lagrange multipliers to choose the number of states for each node of the lattice. Extensive numerical experiments and comparisons with many existing numerical methods confirm the performance claims and the competitiveness of our algorithm. This result places fixed-strike European-style discretely monitored Asian options in the same complexity class as vanilla options. [Copyright &y& Elsevier]

Abstract: In this paper, we use a projected gradient algorithm to solve a nonlinear operator equation with -norm constraint. Gradient iterations with -norm constraints have been studied recently both in the context of inverse problem and of compressed sensing. In this paper, the constrained gradient iteration is implemented via a projected operator. We establish the -norm convergence of sequence constructed by the constrained gradient iteration when . The performance of the method is testified by a numerical example. [Copyright &y& Elsevier]

Abstract: This paper proposes an enhanced cross-entropy (ECE) method to solve dynamic economic dispatch (DED) problem with valve-point effects. The cross-entropy (CE) method, originated from an adaptive variance minimization algorithm for estimating probabilities of rare events, is a generic approach to combinatorial and multi-extremal optimization. Exploration capability of CE algorithm is enhanced in this paper by using chaotic sequence and the resultant ECE is applied to DED with valve-point effects. The performance of the proposed ECE method is rigorously tested for optimality, convergence, robustness and computational efficiency on a 10-unit test system. Additional test cases with different load patterns and increased number of generators are also solved by ECE. Numerical results show that the proposed ECE approach finds high-quality solutions reliably with faster convergence. It outperforms CE and all the previous approaches. [Copyright &y& Elsevier]

Abstract: Many physical phenomena are modelled by nonclassical parabolic boundary value problems with nonlocal boundary conditions. Many different papers studied the second-order parabolic equation, particularly the heat equation subject to the specifications of mass. In this paper, we provide a whole family of new algorithms that improve the CPU time and accuracy of Crandall''s formula shown in [J. Martin-Vaquero, J. Vigo-Aguiar, A note on efficient techniques for the second-order parabolic equation subject to non-local conditions, Appl. Numer. Math. 59 (6) (2009) 1258–1264] (and this algorithm improved the results obtained with BTCS, FTCS or Dufort–Frankel three-level techniques previously used in other works, see [M. Dehghan, Efficient techniques for the second-order parabolic equation subject to nonlocal specifications, Appl. Numer. Math. 52 (2005) 39–62]) with this kind of problems. Other methods got second or fourth order only when , while the new codes got nth order for ; therefore, the new schemes require a smaller storage and CPU time employed than other algorithms. We will study the convergence of the new algorithms and finally we will compare the efficiency of the new methods with some well-known numerical examples. [Copyright &y& Elsevier]

We give an explicit Krasnoselski-Mann type method for finding common solutions of the following system of equilibrium and hierarchical fixed points: {G(x*,y) ≥0, ∀x ϵFix(T), find x* ϵ Fix(T) such that ⟨X* - ƒ (x*), x - x*⟨ ≥ 0, ∀x ϵFix(T), where C is a closed convex subset of a Hilbert space H, G : C × C →ℝ is an equilibrium function, T : C → C is a nonexpansive mapping with Fix(T) its set of fixed points and ƒ : C → C is a ρ-contraction. Our algorithm is constructed and proved using the idea of the paper of [Y. Yao and Y.-C. Liou, 'Weak and strong convergence of Krasnosel'skiĭ-Mann iteration for hierarchical fixed point problems', Inverse Problems 24 (2008), 501-508], in which only the variational inequality problem of finding hierarchically a fixed point of a nonexpansive mapping T with respect to a ρ-contraction ƒ was considered. The paper follows the lines of research of corresponding results of Moudafi and Théra. [ABSTRACT FROM AUTHOR]

In this paper we discuss the convergence behaviour of the nonlinear Uzawa algorithm for solving saddle point problems presented in a recent paper of Cao [Z.H. Cao, Fast Uzawa algorithm for generalized saddle point problems, Appl. Numer. Math. 46 (2003), pp. 157-171]. For a general case, the results on the convergence of the algorithm are given. [ABSTRACT FROM AUTHOR]

As a solution to the frequently reported problem of the high frequencies reconstructed sometimes many iterations after the low frequencies in tomography, we proposed in a recent paper [V. Israel-Jost, Ph. Choquet, and A. Constantinesco, Int. J. Biomed. Imaging, 2006, paper 34043.] a general adaptation that can apply to many algorithms: the incomplete backprojection. We stressed the fact that this type of frequency adapted (FA) algorithm works only when the linear problem of tomography to be solved involves deblurring, i.e., when the point spread functions (PSFs) associated with each voxel are large. Thus, depending on the desired level of detail, a parameter is set to achieve the reconstruction within a small number of iterations. The aim of this paper is to give a mathematical analysis of both the acceleration obtained and the convergence of an FA algorithm derived from the simultaneous algebraic reconstruction technique (SART) algorithm of Andersen and Kak, the so-called FA-SART algorithm. [ABSTRACT FROM AUTHOR]

The paper discusses several versions of the method of shortest residuals, a specific variant of the conjugate gradient algorithm, first introduced by Lemaréchal and Wolfe and discussed by Hestenes in a quadratic case. In the paper we analyze the global convergence of the versions considered. Numerical comparison of these versions of the method of shortest residuals and an implementation of a standard Polak–Ribière conjugate gradient algorithm is also provided. It supports the claim that the method of shortest residuals is a viable technique, competitive to other conjugate gradient algorithms. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a heuristic algorithm, different from the Frank–Wolfe and its modified methods, is introduced for network equilibration. By using the column generation technique and the network equilibrium conditions, the new method need not enumerate initially all feasible paths for all origin/destination (O/D) pairs, but can give all paths used between each O/D pair and the path flows accordingly while the new algorithm obtains an optimal traffic assignment. Some convergence issues of the new method is discussed in this paper. Numerical experiments show that the new method is efficient and robust. [Copyright &y& Elsevier]

In this paper, denoising of smooth ( H10-regular) images is considered. The purpose of the paper is basically twofold. First, to compare the denoising methods based on L1- and L2-fitting. Second, to analyze and realize an active-set method for solving the non-smooth optimization problem arising from the former approach. More precisely, we formulate the algorithm, proof its convergence, and give an efficient numerical realization. Several numerical experiments are presented, where the convergence of the proposed active-set algorithm is studied and the denoising properties of the methods based on L1- and L2-fitting are compared. Also a heuristic method for determining the regularization parameter is presented and tested. [ABSTRACT FROM AUTHOR]

This paper discusses convergence behavior of the nonlinear inexact Uzawa algorithm for solving saddle-point problems presented in a recent paper of Bramble, Pasciak, and Vassilev (SIAM J. Numer. Anal., 34 (1997), pp. 1072­1092). It is shown that this algorithm converges under a condition weaker than that stated in their paper. Key words: saddle-point problems; nonlinear inexact Uzawa algorithm; convergence behavior [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]

As a method of solving the electromagnetic scattering by perfectly conducting cylinders, the discrete singularity method is discussed. For this method, a finite number of singular points is distributed within the scatterer and the wave function composed of a linear combination of solutions (each of which is derived from a helmholtz equation with each single singularity among the many) is matched with the incident wave function on the boundary. The remaining important problem in this method is how to distributed these singularities in order to obtain the accurate solution with faster convergence and with fewer number of singular points for an arbitrary configuration of the scatterer. The purpose of this paper is to present a reasonable solution to this problem. The essential of the method is that by making as unknown quantities, not only the unknown amplitude coefficients involved in the linear combination of the solutions, but also the coordinates of the singularities, the scattered wave is matched on the boundary in the sense of the least squares. This problem is linear in the amplitude coefficient but nonlinear in the singularity coordinate. Thus we solve this problem by using the algorithm by marquardt et al, of a nonlinear optimization process. This paper considers the general description and indicates its effectiveness by showing a few examples of the scattering problem of rectangular cylinders. [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]