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Ya Ping Fang - One of the best experts on this subject based on the ideXlab platform.
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levitin polyak well posedness by perturbations for the split inverse Variational Inequality Problem
Journal of Fixed Point Theory and Applications, 2016Co-Authors: Ya Ping FangAbstract:In this paper, we extend the notion of Levitin–Polyak wellposedness by perturbations to the split inverse Variational Inequality Problem. We derive metric characterizations of Levitin–Polyak wellposedness by perturbations. Under mild conditions, we prove that the Levitin–Polyak well-posedness by perturbations of the split inverse Variational Inequality Problem is equivalent to the existence and uniqueness of its solution.
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Levitin–Polyak well-posedness by perturbations for the split inverse Variational Inequality Problem
Journal of Fixed Point Theory and Applications, 2016Co-Authors: Ya Ping FangAbstract:In this paper, we extend the notion of Levitin–Polyak wellposedness by perturbations to the split inverse Variational Inequality Problem. We derive metric characterizations of Levitin–Polyak wellposedness by perturbations. Under mild conditions, we prove that the Levitin–Polyak well-posedness by perturbations of the split inverse Variational Inequality Problem is equivalent to the existence and uniqueness of its solution.
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Characterizations of Levitin–Polyak well-posedness by perturbations for the split Variational Inequality Problem
Optimization, 2016Co-Authors: Ya Ping FangAbstract:The purpose of this paper is to investigate Levitin–polyak well-posedness by perturbations of the split Variational Inequality Problem in reflexive Banach spaces. Furi-Vignoli-type characterizations are established for the well-posedness. We prove that the weak generalized Levitin–Polyak well-posedness by perturbations is equivalent to the nonemptiness and boundedness of the solution set of the Problem. Finally, we discuss the relations between the Levitin–Polyak well-posedness by perturbations of the split Variational Inequality Problem and the Levitin–Polyak well-posedness by perturbations of the split minimization Problem when the split Variational Inequality Problem arises from the split minimization Problem.
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characterizations of levitin polyak well posedness by perturbations for the split Variational Inequality Problem
Optimization, 2016Co-Authors: Ya Ping FangAbstract:The purpose of this paper is to investigate Levitin–polyak well-posedness by perturbations of the split Variational Inequality Problem in reflexive Banach spaces. Furi-Vignoli-type characterizations are established for the well-posedness. We prove that the weak generalized Levitin–Polyak well-posedness by perturbations is equivalent to the nonemptiness and boundedness of the solution set of the Problem. Finally, we discuss the relations between the Levitin–Polyak well-posedness by perturbations of the split Variational Inequality Problem and the Levitin–Polyak well-posedness by perturbations of the split minimization Problem when the split Variational Inequality Problem arises from the split minimization Problem.
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Well-Posedness of the Split Inverse Variational Inequality Problem
Bulletin of the Malaysian Mathematical Sciences Society, 2015Co-Authors: Ya Ping FangAbstract:The aim of this paper is to study the well-posedness of the split inverse Variational Inequality Problem. We extend the notion of well-posedness to the split inverse Variational Inequality Problem and establish Furi–Vignoli-type characterizations for the well-posedness. We prove that the well-posedness of the split inverse Variational Inequality Problem is equivalent to the existence and uniqueness of its solution.
Poom Kumam - One of the best experts on this subject based on the ideXlab platform.
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algorithms for solving the Variational Inequality Problem over the triple hierarchical Problem
Abstract and Applied Analysis, 2012Co-Authors: Thanyarat Jitpeera, Poom KumamAbstract:This paper discusses the monotone Variational Inequality over the solution set of the Variational Inequality Problem and the fixed point set of a nonexpansive mapping. The strong convergence theorem for the proposed algorithm to the solution is guaranteed under some suitable assumptions.
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weak convergence theorem for monotone mappings and a countable family of nonexpansive mappings
Journal of Computational and Applied Mathematics, 2009Co-Authors: Somyot Plubtieng, Poom KumamAbstract:In this paper, we introduce an iterative process for finding the common element of the set of common fixed points of a countable family of nonexpansive mappings and the set of solutions of the Variational Inequality Problem for an @a-inverse-strongly-monotone mapping. We obtain a weak convergence theorem for a sequence generated by this process. Moreover, we apply our result to the Problem for finding a common element of the set of equilibrium Problems and the set of solutions of the Variational Inequality Problem of a monotone mapping.
K R Kazmi - One of the best experts on this subject based on the ideXlab platform.
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Split general quasi-Variational Inequality Problem
Georgian Mathematical Journal, 2015Co-Authors: K R KazmiAbstract:AbstractIn this paper, we introduce a split general quasi-Variational Inequality Problem which is a natural extension of a split Variational Inequality Problem, quasiVariational and Variational Inequality Problems in Hilbert spaces. Using the projection method, we propose an iterative algorithm for a split general quasi-Variational Inequality Problem and discuss some special cases. Further, we discuss the convergence criteria of these iterative algorithms. The results presented in this paper generalize, unify and improve many previously known results for quasi-Variational and Variational Inequality Problems.
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Split general quasi-Variational Inequality Problem
arXiv: Optimization and Control, 2013Co-Authors: K R KazmiAbstract:In this paper, we introduce a split general quasi-Variational Inequality Problem which is a natural extension of split Variational Inequality Problem, quasi-Variational and Variational Inequality Problems in Hilbert spaces. Using projection method, we propose an iterative algorithm for the split general quasi-Variational Inequality Problem and discuss some its special cases. Further, we discuss the convergence criteria of these iterative algorithms. The results presented in this paper generalize, unify and improve the previously known many results for the quasi-Variational and Variational Inequality Problems.
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split nonconvex Variational Inequality Problem
mathematical sciences, 2013Co-Authors: K R KazmiAbstract:In this paper, we propose a split nonconvex Variational Inequality Problem which is a natural extension of split convex Variational Inequality Problem in two different Hilbert spaces. Relying on the prox-regularity notion, we introduce and establish the convergence of an iterative method for the new split nonconvex Variational Inequality Problem. Further, we also establish the convergence of an iterative method for the split convex Variational Inequality Problem. The results presented in this paper are new and different form the previously known results for nonconvex (convex) Variational Inequality Problems. These results also generalize, unify, and improve the previously known results of this area.
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iterative approximation of a common solution of a split equilibrium Problem a Variational Inequality Problem and a fixed point Problem
Journal of the Egyptian Mathematical Society, 2013Co-Authors: K R Kazmi, S H RizviAbstract:Abstract In this paper, we introduce an iterative method to approximate a common solution of a split equilibrium Problem, a Variational Inequality Problem and a fixed point Problem for a nonexpansive mapping in real Hilbert spaces. We prove that the sequences generated by the iterative scheme converge strongly to a common solution of the split equilibrium Problem, the Variational Inequality Problem and the fixed point Problem for a nonexpansive mapping. The results presented in this paper extend and generalize many previously known results in this research area.
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Convergence and stability of a three-step iterative algorithm for a general quasi-Variational Inequality Problem
Fixed Point Theory and Applications, 2006Co-Authors: K R Kazmi, Mi BhatAbstract:We consider a general quasi-Variational Inequality Problem involving nonlinear, nonconvex and nondifferentiable term in uniformly smooth Banach space. Using retraction mapping and fixed point method, we study the existence of solution of general quasi-Variational Inequality Problem and discuss the convergence analysis and stability of a three-step iterative algorithm for general quasi-Variational Inequality Problem. The theorems presented in this paper generalize, improve, and unify many previously known results in the literature.
Simeon Reich - One of the best experts on this subject based on the ideXlab platform.
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an algorithm for solving the Variational Inequality Problem over the fixed point set of a quasi nonexpansive operator in euclidean space
arXiv: Optimization and Control, 2013Co-Authors: Andrzej Cegielski, Aviv Gibali, Simeon Reich, Rafal ZalasAbstract:This paper is concerned with the Variational Inequality Problem (VIP) over the fixed point set of a quasi-nonexpansive operator. We propose, in particular, an algorithm which entails, at each step, projecting onto a suitably chosen half-space, and prove that the sequences it generates converge to the unique solution of the VIP. We also present an application of our result to a hierarchical optimization Problem.
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an algorithm for solving the Variational Inequality Problem over the fixed point set of a quasi nonexpansive operator in euclidean space
Numerical Functional Analysis and Optimization, 2013Co-Authors: Andrzej Cegielski, Aviv Gibali, Simeon Reich, Rafal ZalasAbstract:This article is concerned with the Variational Inequality Problem VIP(ℱ, Fix(T)): find such that for all z ∈ Fix(T), where T: ℝ n → ℝ n is quasi-nonexpansive, Fix(T) is its nonempty fixed point set, and ℱ: ℝ n → ℝ n is monotone. We propose, in particular, an algorithm which entails, at each step, projecting onto a suitably chosen half-space, and prove that the sequences it generates converge to the unique solution of the VIP. We also present an application of our result to a hierarchical optimization Problem.
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extensions of korpelevich s extragradient method for the Variational Inequality Problem in euclidean space
Optimization, 2012Co-Authors: Yair Censor, Aviv Gibali, Simeon ReichAbstract:We present two extensions of Korpelevich's extragradient method for solving the Variational Inequality Problem (VIP) in Euclidean space. In the first extension, we replace the second orthogonal projection onto the feasible set of the VIP in Korpelevich's extragradient method with a specific subgradient projection. The second extension allows projections onto the members of an infinite sequence of subsets which epi-converges to the feasible set of the VIP. We show that in both extensions the convergence of the method is preserved and present directions for further research.
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algorithms for the split Variational Inequality Problem
Numerical Algorithms, 2012Co-Authors: Yair Censor, Aviv Gibali, Simeon ReichAbstract:We propose a prototypical Split Inverse Problem (SIP) and a new Variational Problem, called the Split Variational Inequality Problem (SVIP), which is a SIP. It entails finding a solution of one inverse Problem (e.g., a Variational Inequality Problem (VIP)), the image of which under a given bounded linear transformation is a solution of another inverse Problem such as a VIP. We construct iterative algorithms that solve such Problems, under reasonable conditions, in Hilbert space and then discuss special cases, some of which are new even in Euclidean space.
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strong convergence of subgradient extragradient methods for the Variational Inequality Problem in hilbert space
Optimization Methods & Software, 2011Co-Authors: Yair Censor, Aviv Gibali, Simeon ReichAbstract:We study two projection algorithms for solving the Variational Inequality Problem in Hilbert space. One algorithm is a modified subgradient extragradient method in which an additional projection onto the intersection of two half-spaces is employed. Another algorithm is based on the shrinking projection method. We establish strong convergence theorems for both algorithms.
Aviv Gibali - One of the best experts on this subject based on the ideXlab platform.
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an algorithm for solving the Variational Inequality Problem over the fixed point set of a quasi nonexpansive operator in euclidean space
arXiv: Optimization and Control, 2013Co-Authors: Andrzej Cegielski, Aviv Gibali, Simeon Reich, Rafal ZalasAbstract:This paper is concerned with the Variational Inequality Problem (VIP) over the fixed point set of a quasi-nonexpansive operator. We propose, in particular, an algorithm which entails, at each step, projecting onto a suitably chosen half-space, and prove that the sequences it generates converge to the unique solution of the VIP. We also present an application of our result to a hierarchical optimization Problem.
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an algorithm for solving the Variational Inequality Problem over the fixed point set of a quasi nonexpansive operator in euclidean space
Numerical Functional Analysis and Optimization, 2013Co-Authors: Andrzej Cegielski, Aviv Gibali, Simeon Reich, Rafal ZalasAbstract:This article is concerned with the Variational Inequality Problem VIP(ℱ, Fix(T)): find such that for all z ∈ Fix(T), where T: ℝ n → ℝ n is quasi-nonexpansive, Fix(T) is its nonempty fixed point set, and ℱ: ℝ n → ℝ n is monotone. We propose, in particular, an algorithm which entails, at each step, projecting onto a suitably chosen half-space, and prove that the sequences it generates converge to the unique solution of the VIP. We also present an application of our result to a hierarchical optimization Problem.
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extensions of korpelevich s extragradient method for the Variational Inequality Problem in euclidean space
Optimization, 2012Co-Authors: Yair Censor, Aviv Gibali, Simeon ReichAbstract:We present two extensions of Korpelevich's extragradient method for solving the Variational Inequality Problem (VIP) in Euclidean space. In the first extension, we replace the second orthogonal projection onto the feasible set of the VIP in Korpelevich's extragradient method with a specific subgradient projection. The second extension allows projections onto the members of an infinite sequence of subsets which epi-converges to the feasible set of the VIP. We show that in both extensions the convergence of the method is preserved and present directions for further research.
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The Split Common Null Point Problem
arXiv: Optimization and Control, 2012Co-Authors: Charles Byrne, Yair Censor, Aviv GibaliAbstract:We introduce and study the Split Common Null Point Problem (SCNPP) for set-valued maximal monotone mappings in Hilbert spaces. This Problem generalizes our Split Variational Inequality Problem (SVIP) [Y. Censor, A. Gibali and S. Reich, Algorithms for the split Variational Inequality Problem, Numerical Algorithms 59 (2012), 301{ 323]. The SCNPP with only two set-valued mappings entails nding a zero of a maximal monotone mapping in one space, the image of which
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algorithms for the split Variational Inequality Problem
Numerical Algorithms, 2012Co-Authors: Yair Censor, Aviv Gibali, Simeon ReichAbstract:We propose a prototypical Split Inverse Problem (SIP) and a new Variational Problem, called the Split Variational Inequality Problem (SVIP), which is a SIP. It entails finding a solution of one inverse Problem (e.g., a Variational Inequality Problem (VIP)), the image of which under a given bounded linear transformation is a solution of another inverse Problem such as a VIP. We construct iterative algorithms that solve such Problems, under reasonable conditions, in Hilbert space and then discuss special cases, some of which are new even in Euclidean space.
