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In this paper, a new appropriate diagonal matrix estimation of the Hessian is introduced by minimizing the Byrd and Nocedal function subject to the weak secant equation. The Hessian estimate is used to correct the framework of a nonmonotone trust region algorithm with the regularized quasi-Newton method. Moreover, to counteract the adverse effect of monotonicity, we introduce a new nonmonotone strategy. The global and superlinear convergence of the suggested algorithm is established under some standard conditions. The numerical experiments on unconstrained optimization test functions show that the new algorithm is efficient and robust. [ABSTRACT FROM AUTHOR]

In this paper, we study the generalized multiple-set split feasibility problem including the common fixed-point problem for a finite family of generalized demimetric mappings and the monotone inclusion problem in 2-uniformly convex and uniformly smooth Banach spaces. We propose an inertial Halpern-type iterative algorithm for obtaining a solution of the problem and derive a strong convergence theorem for the algorithm. Then, we apply our convergence results to the convex minimization problem, the variational inequality problem, the multiple-set split feasibility problem and the split common null-point problem in Banach spaces. [ABSTRACT FROM AUTHOR]

This paper provides convergence analysis of some variants of the hybrid extragradient algorithm (HEA) in Hilbert spaces. We employ the HEA to compute the common solution of the equilibrium problem and split fixed-point problem associated with the finite families of k -demicontractive mappings. We also incorporate appropriate numerical results concerning the viability of the proposed variants with respect to various real-world applications. [ABSTRACT FROM AUTHOR]

In this paper, we propose two inertial algorithms with a new self-adaptive step size for approximating a solution of the split common null-point problem in the framework of Banach spaces. The step sizes are adaptively updated over each iteration by a simple process without the prior knowledge of the operator norm of the bounded linear operator. Under suitable conditions, we prove the weak-convergence results for the proposed algorithms in p-uniformly convex and uniformly smooth Banach spaces. Finally, we give several numerical results in both finite- and infinite-dimensional spaces to illustrate the efficiency and advantage of the proposed methods over some existing methods. Also, data classifications of heart diseases and diabetes mellitus are presented as the applications of our methods. [ABSTRACT FROM AUTHOR]

In this paper, we transform the classical linear discriminant analysis (LDA) into a smooth difference-of-convex optimization problem. Then, a new difference-of-convex algorithm with extrapolation is introduced and the convergence of the algorithm is established. Finally, for a face recognition problem, the proposed algorithm achieves better classification performance compared with several current algorithms in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we establish the stability and strong convergence theorems, for the three-step iteration with perturbations for a T-Ciric quasicontraction, in the environment of the CAT(0) space. Finally, an application to the integral-type contraction and an example are shown. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a simple and easily computable algorithm for finding a common solution to split-equilibrium problems and fixed-point problems in the framework of real Hilbert spaces. New self-adaptive step sizes are adopted for the avoidance of Lipschitz constants that are not practically implemented. Furthermore, an inertial term is incorporated to speed up the rate of convergence, a condition that is very desirable in applications. A strong convergence is obtained under some mild assumptions, which is not limited to the fact that the bifunctions are pseudomonotone operators. This condition is better, weaker, and more general than being strongly pseudomonotone or monotone. Our result improves and extends already announced results in this direction of research. [ABSTRACT FROM AUTHOR]

The generalized Schwarz algorithm for a class of elliptic quasi-variational inequalities related to impulse control problems is studied in this paper. The principal result is to prove the error estimate in L ∞ -norm for m subdomains with overlapping nonmatching grids. This approach combines the geometrical convergence and the uniform convergence. [ABSTRACT FROM AUTHOR]

In this paper, a simple proof of the convergence of the recent iterative algorithm by relaxed (u , v) -cocoercive mappings due to Imnang (J. Inequal. Appl. 2013:249, 2013) is presented. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of a class of generalized nonexpansive mappings called generalized nearly asymptotically nonexpansive mappings and to show that it properly includes the class of nearly asymptotically nonexpansive mappings. We investigate the problem of approximating a common element of the set of solutions of a system of generalized nonlinear variational-like inclusions involving P-η-accretive mappings and of the set of fixed points of a generalized nearly asymptotically nonexpansive mapping. To this end, we suggest a new iterative algorithm with mixed errors. As an application of the obtained equivalence, we prove the strong convergence and stability of the sequence generated by the proposed iterative algorithm to a common point of the two sets mentioned above. [ABSTRACT FROM AUTHOR]

This paper aims at proposing an iterative algorithm for finding an element in the intersection of the solutions set of a system of variational inclusions and the fixed-points set of a total uniformly L-Lipschitzian mapping. Applying the concepts of graph convergence and the resolvent operator associated with an Ĥ-accretive mapping, a new equivalence relationship between graph convergence and resolvent-operator convergence of a sequence of Ĥ-accretive mappings is established. As an application of the obtained equivalence relationship, the strong convergence of the sequence generated by our proposed iterative algorithm to a common point of the above two sets is proved under some suitable hypotheses imposed on the parameters and mappings. At the same time, the notion of H (⋅ , ⋅) -accretive mapping that appeared in the literature, where H (⋅ , ⋅) is an α, β-generalized accretive mapping, is also investigated and analyzed. We show that the notions H (⋅ , ⋅) -accretive and Ĥ-accretive operators are actually the same, and point out some comments on the results concerning them that are available in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we define a new concept of left and right coordinate affine of a directed graph and then employ it to introduce a new accelerated common fixed point algorithm for a countable family of G-nonexpansive mappings in a real Hilbert space with a graph. We prove, under certain conditions, weak convergence theorems for the proposed algorithm. As applications, we also apply our results to solve convex minimization and image restoration problems. Moreover, we show that our algorithm provides better convergence behavior than other methods in the literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce and study an inertial hybrid iterative method for solving generalized equilibrium problems involving Bregman relatively nonexpansive mappings in Banach spaces. We study the strong convergence for the proposed algorithm. Finally, we list some consequences and computational example to emphasize the efficiency and relevancy of main result. [ABSTRACT FROM AUTHOR]

The multiple-sets split feasibility problem is the generalization of split feasibility problem, which has been widely used in fuzzy image reconstruction and sparse signal processing systems. In this paper, we present an inertial relaxed algorithm to solve the multiple-sets split feasibility problem by using an alternating inertial step. The advantage of this algorithm is that the choice of stepsize is determined by Armijo-type line search, which avoids calculating the norms of operators. The weak convergence of the sequence obtained by our algorithm is proved under mild conditions. In addition, the numerical experiments are given to verify the convergence and validity of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a second-order hyperbolic equation is solved by a two-grid algorithm combined with the expanded mixed finite element method. The error estimate of the expanded mixed finite element method with discrete-time scheme is demonstrated. Moreover, we present a two-grid method and analyze its convergence. It is shown that the algorithm can achieve asymptotically optimal approximation as long as the mesh sizes satisfy H = O (h 1 2) . Finally, some numerical experiments are provided to illustrate the efficiency and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new iterative algorithm for solving the multiple-sets split feasibility problem (MSSFP for short) and the split equality fixed point problem (SEFPP for short) with firmly quasi-nonexpansive operators or nonexpansive operators in real Hilbert spaces. Under mild conditions, we prove strong convergence theorems for the algorithm by using the projection method and the properties of projection operators. The result improves and extends the corresponding ones announced by some others in the earlier and recent literature. [ABSTRACT FROM AUTHOR]

In this paper, we suggest and analyze an iterative algorithm to approximate a common solution of a hierarchical fixed point problem for nonexpansive mappings, a system of variational inequalities, and a split equilibrium problem in Hilbert spaces. Under some suitable conditions imposed on the sequences of parameters, we prove that the sequence generated by the proposed iterative method converges strongly to a common element of the solution set of these three kinds of problems. The results obtained here extend and improve the corresponding results of the relevant literature. [ABSTRACT FROM AUTHOR]

In this paper, we propose a modified proximal point algorithm based on the Thakur iteration process to approximate the common element of the set of solutions of convex minimization problems and the fixed points of two nearly asymptotically quasi-nonexpansive mappings in the framework of CAT (0) spaces. We also prove the Δ-convergence of the proposed algorithm. We also provide an application and numerical result based on our proposed algorithm as well as the computational result by comparing our modified iteration with previously known Sahu's modified iteration. [ABSTRACT FROM AUTHOR]

In this paper, using a Bregman distance technique, we introduce a new single projection process for approximating a common element in the set of solutions of variational inequalities involving a pseudo-monotone operator and the set of common fixed points of a finite family of Bregman quasi-nonexpansive mappings in a real reflexive Banach space. The stepsize of our algorithm is determined by a self-adaptive method, and we prove a strong convergence result under certain mild conditions. We further give some applications of our result to a generalized Nash equilibrium problem and bandwidth allocation problems. We also provide some numerical experiments to illustrate the performance of our proposed algorithm using various convex functions and compare this algorithm with other algorithms in the literature. [ABSTRACT FROM AUTHOR]

Recent studies show that the filter method has good numerical performance for nonlinear complementary problems (NCPs). Their approach is to reformulate an NCP as a constrained optimization solved by filter algorithms. However, they can only prove that the iterative sequence converges to the KKT point of the constrained optimization. In this paper, we investigate the relation between the KKT point of the constrained optimization and the solution of the NCP. First, we give several sufficient conditions under which the KKT point of the constrained optimization is the solution of the NCP; second, we define regular conditions and regular point which include and generalize the previous results; third, we prove that the level sets of the objective function of the constrained optimization are bounded for a strongly monotone function or a uniform P-function; finally, we present some examples to verify the previous results. [ABSTRACT FROM AUTHOR]

A Polak–Ribière–Polyak (PRP) algorithm is one of the oldest and popular conjugate gradient algorithms for solving nonlinear unconstrained optimization problems. In this paper, we present a q-variant of the PRP (q-PRP) method for which both the sufficient and conjugacy conditions are satisfied at every iteration. The proposed method is convergent globally with standard Wolfe conditions and strong Wolfe conditions. The numerical results show that the proposed method is promising for a set of given test problems with different starting points. Moreover, the method reduces to the classical PRP method as the parameter q approaches 1. [ABSTRACT FROM AUTHOR]

In this paper, we propose two iterative schemes for approximating solutions of split common fixed point problems in multiple linear operators case. The first algorithm implements the Krasnosel'skiĭ–Mann iteration with an inertial effect for which the weak convergence is established under mild assumptions. With the tool of nearly contractive mappings, we introduce a viscosity-type iteration which ensures strong convergence. We apply our results to solve a multiple split monotone variational inclusion problem. A numerical example is given to demonstrate the efficiency of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new inertial self-adaptive projection method for finding a common element in the set of solution of pseudomonotone variational inequality problem and set of fixed point of a pseudocontractive mapping in real Hilbert spaces. The self-adaptive technique ensures the convergence of the algorithm without any prior estimate of the Lipschitz constant. With the aid of Moudafi's viscosity approximation method, we prove a strong convergence result for the sequence generated by our algorithm under some mild conditions. We also provide some numerical examples to illustrate the accuracy and efficiency of the algorithm by comparing with other recent methods in the literature. [ABSTRACT FROM AUTHOR]

The proximal gradient method is a highly powerful tool for solving the composite convex optimization problem. In this paper, firstly, we propose inexact inertial acceleration methods based on the viscosity approximation and proximal scaled gradient algorithm to accelerate the convergence of the algorithm. Under reasonable parameters, we prove that our algorithms strongly converge to some solution of the problem, which is the unique solution of a variational inequality problem. Secondly, we propose an inexact alternated inertial proximal point algorithm. Under suitable conditions, the weak convergence theorem is proved. Finally, numerical results illustrate the performances of our algorithms and present a comparison with related algorithms. Our results improve and extend the corresponding results reported by many authors recently. [ABSTRACT FROM AUTHOR]

In this paper we study the bounded perturbation resilience of the extragradient and the subgradient extragradient methods for solving a variational inequality (VI) problem in real Hilbert spaces. This is an important property of algorithms which guarantees the convergence of the scheme under summable errors, meaning that an inexact version of the methods can also be considered. Moreover, once an algorithm is proved to be bounded perturbation resilience, superiorization can be used, and this allows flexibility in choosing the bounded perturbations in order to obtain a superior solution, as well explained in the paper. We also discuss some inertial extragradient methods. Under mild and standard assumptions of monotonicity and Lipschitz continuity of the VI's associated mapping, convergence of the perturbed extragradient and subgradient extragradient methods is proved. In addition we show that the perturbed algorithms converge at the rate of $O(1/t)$ . Numerical illustrations are given to demonstrate the performances of the algorithms. [ABSTRACT FROM AUTHOR]

This paper presents an extragradient-like method for solving a pseudomonotone equilibrium problem with a Lipschitz-type condition on Hadamard manifolds. The algorithm only needs to know the existence of the Lipschitz-type constants of the bifunction, and the stepsize of each iteration is determined by the adjacent iterations. Convergence of the algorithm is analyzed, and its application to variational inequalities is also provided. Finally, several experiments are made to verify the effectiveness of the algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we introduce blending functions of Lupaş q-Bernstein operators with shifted knots for constructing q-Bézier curves and surfaces. We study the nature of degree elevation and degree reduction for Lupaş q-Bézier Bernstein functions with shifted knots for t ∈ [ a [ μ ] q + b , [ μ ] q + a [ μ ] q + b ] . For the parameters a = b = 0 , we get Lupaş q-Bézier curves defined on [ 0 , 1 ] . We show that Lupaş q-Bernstein functions with shifted knots are tangent to fore-and-aft of its polygon at end points. We present a de Casteljau algorithm to compute Bernstein Bézier curves and surfaces with shifted knots. The new curves have some properties similar to q-Bézier curves. Similarly, we discuss the properties of the tensor product for Lupaş q-Bézier surfaces with shifted knots over the rectangular domain. [ABSTRACT FROM AUTHOR]

The subspace technique has been widely used to solve unconstrained/constrained optimization problems and there exist many results that have been obtained. In this paper, a subspace algorithm combining with limited memory BFGS update is proposed for large-scale nonsmooth optimization problems with box-constrained conditions. This algorithm can ensure that all iteration points are feasible and the sequence of objective functions is decreasing. Moreover, rapid changes in the active set are allowed. The global convergence is established under some suitable conditions. Numerical results show that this method is very effective for large-scale nonsmooth box-constrained optimization, where the largest dimension of the test problems is 11,000 variables. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an algorithm for solving classical variational inequalities problem with Lipschitz continuous and monotone mapping in Banach space. We modify the subgradient extragradient methods with a new and simple iterative step size, the strong convergence of algorithm is established without the knowledge of the Lipschitz constant of the mapping. Finally, a numerical experiment is presented to show the efficiency and advantage of the proposed algorithm. Our results generalize some of the work in Hilbert spaces to Banach spaces. [ABSTRACT FROM AUTHOR]

For a variational inequality problem, the inertial projection and contraction method have been studied. It has a weak convergence result. In this paper, we propose a strong convergence iterative method for finding a solution of a variational inequality problem with a monotone mapping by projection and contraction method and inertial hybrid algorithm. Our result can be used to solve other related problems in Hilbert spaces. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new class of variational inequality problems, say, uncertain variational inequality problems based on uncertainty theory in finite Euclidean spaces $R^{n}$. It can be viewed as another extension of classical variational inequality problems besides stochastic variational inequality problems. Note that both stochastic variational inequality problems and uncertain variational inequality problems involve uncertainty in the real world, thus they have no conceptual solutions. Hence, in order to solve uncertain variational inequality problems, we introduce the expected value of uncertain variables (vector). Then we convert it into a classical deterministic variational inequality problem, which can be solved by many algorithms that are developed on the basis of gap functions. Thus the core of this paper is to discuss under what conditions we can convert the expected value model of uncertain variational inequality problems into deterministic variational inequality problems. Finally, as an application, we present an example in a noncooperation game from economics. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to propose an algorithm to solve the split common fixed point problems for total asymptotically strict pseudocontraction mappings in Hilbert spaces. Without the assumption of semi-compactness on the mappings, the iterative scheme is shown to converge strongly to a split common fixed point of such mappings. The results presented in the paper improve and extend some recent corresponding results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a proximal point iterative algorithm with general errors for monotone mappings in Banach spaces. We prove that the proposed algorithm converges strongly to a proximal point for monotone mappings. Our theorems in this paper improve and unify most of the results that have been proposed for this important class of nonlinear mappings. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and analyze a general iterative algorithm for finding a common solution of a finite family of mixed equilibrium problems, a general system of generalized equilibria and a fixed point problem of nonexpansive mappings in a real Hilbert space. Under some appropriate conditions, we derive the strong convergence of the sequence generated by the proposed algorithm to a common solution, which also solves some optimization problem. The result presented in this paper improves and extends some corresponding ones in the earlier and recent literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and analyze a multi-step hybrid extragradient algorithm by combining Korpelevich's extragradient method, the viscosity approximation method, the hybrid steepest-descent method, Mann's iteration method and the gradient-projection method (GPM) with regularization in the setting of infinite-dimensional Hilbert spaces. It is proven that, under appropriate assumptions, the proposed algorithm converges strongly to a solution of the convex minimization problem (CMP) with constraints of several problems: finitely many generalized mixed equilibrium problems (GMEPs), finitely many variational inclusions, and the fixed point problem of a strictly pseudocontractive mapping. In the meantime, we also prove the strong convergence of the proposed algorithm to the unique solution of a hierarchical variational inequality problem (over the fixed point set of a strictly pseudocontractive mapping) with constraints of finitely many GMEPs, finitely many variational inclusions and the CMP. The results presented in this paper improve and extend the corresponding results announced by many others. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and analyze a relaxed iterative algorithm by virtue of Korpelevich's extragradient method, the viscosity approximation method, the hybrid steepest-descent method, the regularization method, and the averaged mapping approach to the gradient-projection algorithm. It is proven that under appropriate assumptions, the proposed algorithm converges strongly to a common element of the fixed point set of infinitely many nonexpansive mappings, the solution set of finitely many generalized mixed equilibrium problems (GMEPs), the solution set of finitely many variational inclusions and the set of minimizers of convex minimization problem (CMP), which is just a unique solution of a triple hierarchical variational inequality (THVI) in a real Hilbert space. In addition, we also consider the application of the proposed algorithm to solving a hierarchical fixed point problem with constraints of finitely many GMEPs, finitely many variational inclusions, and CMP. The results obtained in this paper improve and extend the corresponding results announced by many others. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce and study a class of new general systems of set-valued variational inclusions involving relative (A,η)-maximal monotone operators in Hilbert spaces. By using the generalized resolvent operator technique associated with relative (A,η)-maximal monotone operators, we also construct some new iterative algorithms for finding approximation solutions to the general systems of set-valued variational inclusions and prove the convergence of the sequences generated by the algorithms. The results presented in this paper improve and extend some known results in the literature. [ABSTRACT FROM AUTHOR]

This paper presents a practicable regional division and cut algorithm for minimizing the sum of linear fractional functions over a polyhedron. In the algorithm, by using an equivalent problem (P) of the original problem, the proposed division operation generalizes the usual standard bisection, and the deleting and reduction operations can cut away a large part of the current investigated region in which the global optimal solution of (P) does not exist. The main computation involves solving a sequence of univariate equations with strict monotonicity. The proposed algorithm is convergent to the global minimum through the successive refinement of the solutions of a series of univariate equations. Numerical results are given to show the feasibility and effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

It is known that the concept of ratio monotonicity is closely related to log-convexity and log-concavity. In this paper, by exploring the log-behavior properties of a new combinatorial sequence defined by Z.-W. Sun, we completely solve a conjecture on ratio monotonicity by him. [ABSTRACT FROM AUTHOR]

Let $A_{1}, A_{2},\ldots, A_{k}$ be nonnegative matrices. In this paper, some upper bounds for the spectral radius $\rho(A_{1}\circ A_{2}\circ\cdots\circ A_{k})$ are proposed. These bounds generalize some existing results, and comparisons between these bounds are also considered. [ABSTRACT FROM AUTHOR]

The split feasibility problem (SFP) is finding a point $x\in C$ such that $Ax\in Q$ , where C and Q are nonempty closed convex subsets of Hilbert spaces $H_{1}$ and $H_{2}$ , and $A:H_{1}\rightarrow H_{2}$ is a bounded linear operator. Byrne's CQ algorithm is an effective algorithm to solve the SFP, but it needs to compute $\|A\|$ , and sometimes $\|A\| $ is difficult to work out. López introduced a choice of stepsize $\lambda_{n}$ , $\lambda_{n}=\frac{\rho_{n}f(x_{n})}{\|\nabla f(x_{n})\| ^{2}}$ , $0<\rho_{n}<4$ . However, he only obtained weak convergence theorems. In order to overcome the drawbacks, in this paper, we first provide a regularized CQ algorithm without computing $\|A\|$ to find the minimum-norm solution of the SFP and then obtain a strong convergence theorem. [ABSTRACT FROM AUTHOR]

In this paper, a modified BFGS algorithm is proposed for unconstrained optimization. The proposed algorithm has the following properties: (i) a nonmonotone line search technique is used to obtain the step size $\alpha_{k}$ to improve the effectiveness of the algorithm; (ii) the algorithm possesses not only global convergence but also superlinear convergence for generally convex functions; (iii) the algorithm produces better numerical results than those of the normal BFGS method. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a viscosity iterative algorithm for the implicit midpoint rule of nonexpansive mappings in uniformly smooth spaces. Under some appropriate conditions on the parameters, we prove some strong convergence theorems. As applications, we apply our main results to solving fixed point problems of strict pseudocontractive mappings, variational inequality problems in Banach spaces and equilibrium problems in Hilbert spaces. Finally, we give some numerical examples for supporting our main results. [ABSTRACT FROM AUTHOR]

In this paper, we present a QP-free algorithm for nonlinear semidefinite programming. At each iteration, the search direction is yielded by solving two systems of linear equations with the same coefficient matrix; $l_{1}$ penalty function is used as merit function for line search, the step size is determined by Armijo type inexact line search. The global convergence of the proposed algorithm is shown under suitable conditions. Preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study iterative algorithms for solving split mixed equilibrium problems and fixed point problems of λ-hybrid multivalued mappings in real Hilbert spaces and prove that the proposed iterative algorithm converges weakly to a common solution of the considered problems. We also provide an example to illustrate the convergence behavior of the proposed iteration process. [ABSTRACT FROM AUTHOR]

This paper presents a linear decomposition approach for a class of nonconvex programming problems by dividing the input space into polynomially many grids. It shows that under certain assumptions the original problem can be transformed and decomposed into a polynomial number of equivalent linear programming subproblems. Based on solving a series of liner programming subproblems corresponding to those grid points we can obtain the near-optimal solution of the original problem. Compared to existing results in the literature, the proposed algorithm does not require the assumptions of quasi-concavity and differentiability of the objective function, and it differs significantly giving an interesting approach to solving the problem with a reduced running time. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two iterative algorithms for finding the solution of the sum of two monotone operators by using hybrid projection methods and shrinking projection methods. Under some suitable conditions, we prove strong convergence theorems of such sequences to the solution of the sum of an inverse-strongly monotone and a maximal monotone operator. Finally, we present a numerical result of our algorithm which is defined by the hybrid method. [ABSTRACT FROM AUTHOR]

This paper introduces a new extragradient-type method to solve the multiple-sets split equality problem (MSSEP). Under some suitable conditions, the strong convergence of an algorithm can be verified in the infinite-dimensional Hilbert spaces. Moreover, several numerical results are given to show the effectiveness of our algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a modified feasible semi-smooth asymptotically Newton method for nonlinear complementarity problems is proposed. The global convergence of the method and superlinear convergence are proved under some suitable assumptions. Numerical experiments are included to highlight the efficacy of the modified algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of weakly nonlinear complementarity problems (WNCP) with large sparse matrix. We present an accelerated modulus-based matrix splitting algorithm by reformulating the WNCP as implicit fixed point equations based on two splittings of the system matrixes. We show that, if the system matrix is a P-matrix, then under some mild conditions the sequence generated by the algorithm is convergent to the solution of WNCP. [ABSTRACT FROM AUTHOR]