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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 of split minimization problems
Journal of Fixed Point Theory and Applications, 2017Co-Authors: Ying-kang Liu, Ya Ping FangAbstract:In this paper, we extend well-Posedness notions to the split minimization problem which entails finding a solution of one minimization problem such that its image under a given bounded linear transformation is a solution of another minimization problem. We prove that the split minimization problem in the setting of finite-dimensional spaces is Levitin–Polyak well-posed by perturbations provided that its solution set is nonempty and bounded. We also extend well-Posedness notions to the split inclusion problem. We show that the well-Posedness of the split convex minimization problem is equivalent to the well-Posedness of the equivalent split inclusion 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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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.
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Levitin–Polyak well-Posedness by perturbations of inverse variational inequalities
Optimization Letters, 2011Co-Authors: Ya Ping FangAbstract:The purpose of this paper is to investigate Levitin–Polyak type well-Posedness for inverse variational inequalities. We establish some metric characterizations of Levitin–Polyak α-well-Posedness by perturbations. Under suitable conditions, we prove that Levitin–Polyak well-Posedness by perturbations of an inverse variational inequality is equivalent to the existence and uniqueness of its solution. Moreover, we show that Levitin–Polyak well-Posedness by perturbations of an inverse variational inequality is equivalent to Levitin–Polyak well-Posedness by perturbations of an enlarged classical variational inequality.
Nan-jing Huang - One of the best experts on this subject based on the ideXlab platform.
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Well-Posedness of Hemivariational Inequalities and Inclusion Problems
Taiwanese Journal of Mathematics, 2011Co-Authors: Yi-bin Xiao, Nan-jing Huang, Mu-ming WongAbstract:In the present paper, we generalize the concept of well-Posedness to a hemivariational inequality, give some metric characterizations of the wellposed hemivariational inequality, and derive some conditions under which the hemivariational inequality is strongly well-posed in the generalized sense. Also, we show that the well-Posedness of the hemivariational inequality is equivalent to the well-Posedness of the corresponding inclusion problem.
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Well-Posedness of Systems of Equilibrium Problems
Taiwanese Journal of Mathematics, 2010Co-Authors: Ya Ping Fang, Nan-jing Huang, Mu-ming WongAbstract:In this paper we introduce the concepts of well-Posedness and generalized well-Posedness for a system of equilibrium problems. We derive a metric characterization of well-Posedness by considering the diameter of approximating solution set and a Furi-Vignoli type characterization of generalized well-Posedness by considering the Kuratowski noncompactness measure of approximating solution set. Under suitable conditions, we prove that the well-Posedness of a system of equilibrium problems is equivalent to the existence and uniqueness of its solution.
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Well-Posedness by perturbations of mixed variational inequalities in Banach spaces
European Journal of Operational Research, 2010Co-Authors: Ya Ping Fang, Nan-jing Huang, Jen-chih YaoAbstract:In this paper, we consider an extension of the notion of well-Posedness by perturbations, introduced by Zolezzi for a minimization problem, to a mixed variational inequality problem in a Banach space. We establish some metric characterizations of the well-Posedness by perturbations. We also show that under suitable conditions, the well-Posedness by perturbations of a mixed variational inequality problem is equivalent to the well-Posedness by perturbations of a corresponding inclusion problem and a corresponding fixed point problem. Also, we derive some conditions under which the well-Posedness by perturbations of a mixed variational inequality is equivalent to the existence and uniqueness of its solution.
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Well-Posedness for vector quasi-equilibrium problems with applications
Journal of Industrial & Management Optimization, 2009Co-Authors: Nan-jing Huang, Xian-jun Long, Chang-wen ZhaoAbstract:In this paper, we introduce the concept of well-Posedness for the vector quasi-equilibrium problem. We obtain some necessary and sufficient conditions for well-Posedness of vector quasi-equilibrium problems. As applications, we investigate the well-Posedness for vector quasi-variational inequality problems and vector quasi-optimization problems.
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Levitin-Polyak Well-Posedness for Equilibrium Problems with Functional Constraints
Journal of Inequalities and Applications, 2008Co-Authors: Xian-jun Long, Nan-jing Huang, Kok Lay TeoAbstract:We generalize the notions of Levitin-Polyak well-Posedness to an equilibrium problem with both abstract and functional constraints. We introduce several types of (generalized) Levitin-Polyak well-Posedness. Some metric characterizations and sufficient conditions for these types of well-Posedness are obtained. Some relations among these types of well-Posedness are also established under some suitable conditions.
Jian-wen Peng - One of the best experts on this subject based on the ideXlab platform.
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Scalarization and pointwise well-Posedness for set optimization problems
Journal of Global Optimization, 2015Co-Authors: Xian-jun Long, Jian-wen Peng, Zai-yun PengAbstract:In this paper, we consider three kinds of pointwise well-Posedness for set optimization problems. We establish some relations among the three kinds of pointwise well-Posedness. By virtue of a generalized nonlinear scalarization function, we obtain the equivalence relations between the three kinds of pointwise well-Posedness for set optimization problems and the well-Posedness of three kinds of scalar optimization problems, respectively.
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Generalized B-Well-Posedness for Set Optimization Problems
Journal of Optimization Theory and Applications, 2012Co-Authors: Xian-jun Long, Jian-wen PengAbstract:This paper aims at studying the generalized well-Posedness in the sense of Bednarczuk for set optimization problems with set-valued maps. Three kinds of B-well-Posedness for set optimization problems are introduced. Some relations among the three kinds of B-well-Posedness are established. Necessary and sufficient conditions of well-Posedness for set optimization problems are obtained.
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α-Well-Posedness for Quasivariational Inequality Problems
Abstract and Applied Analysis, 2012Co-Authors: Jian-wen Peng, Jing TangAbstract:We introduce and study the concepts of α-well-Posedness and L-α-well-Posedness for quasivariational inequality problems having a unique solution and the concepts of α-well-Posedness in the generalized sense and L-α-well-Posedness in the generalized sense for quasivariational inequality problems having more than one solution. We present some necessary and/or sufficient conditions for the various kinds of well-Posedness to occur. Our results generalize and strengthen previously known results for quasivariational inequality problems.
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The Well-Posedness for Multiobjective Generalized Games
Journal of Optimization Theory and Applications, 2011Co-Authors: Jian-wen PengAbstract:In this paper, the new notions of the generalized Tykhonov well-Posedness for multiobjective generalized games are investigated. By using the gap functions of the multiobjective generalized games, we establish the equivalent relationship between the generalized Tykhonov well-Posedness of the multiobjective generalized games and that of the minimization problems. Some metric characterizations for the generalized Tykhonov well-Posedness of the multiobjective generalized games are also presented.
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-Well-Posedness for Mixed Quasi Variational-Like Inequality Problems
Abstract and Applied Analysis, 2011Co-Authors: Jian-wen Peng, Jing TangAbstract:The concepts of
Jing Tang - One of the best experts on this subject based on the ideXlab platform.
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α-Well-Posedness for Quasivariational Inequality Problems
Abstract and Applied Analysis, 2012Co-Authors: Jian-wen Peng, Jing TangAbstract:We introduce and study the concepts of α-well-Posedness and L-α-well-Posedness for quasivariational inequality problems having a unique solution and the concepts of α-well-Posedness in the generalized sense and L-α-well-Posedness in the generalized sense for quasivariational inequality problems having more than one solution. We present some necessary and/or sufficient conditions for the various kinds of well-Posedness to occur. Our results generalize and strengthen previously known results for quasivariational inequality problems.
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-Well-Posedness for Mixed Quasi Variational-Like Inequality Problems
Abstract and Applied Analysis, 2011Co-Authors: Jian-wen Peng, Jing TangAbstract:The concepts of
Jen-chih Yao - One of the best experts on this subject based on the ideXlab platform.
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Well-Posedness by perturbations of mixed variational inequalities in Banach spaces
European Journal of Operational Research, 2010Co-Authors: Ya Ping Fang, Nan-jing Huang, Jen-chih YaoAbstract:In this paper, we consider an extension of the notion of well-Posedness by perturbations, introduced by Zolezzi for a minimization problem, to a mixed variational inequality problem in a Banach space. We establish some metric characterizations of the well-Posedness by perturbations. We also show that under suitable conditions, the well-Posedness by perturbations of a mixed variational inequality problem is equivalent to the well-Posedness by perturbations of a corresponding inclusion problem and a corresponding fixed point problem. Also, we derive some conditions under which the well-Posedness by perturbations of a mixed variational inequality is equivalent to the existence and uniqueness of its solution.
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WELL-Posedness FOR VECTOR QUASIEQUILIBRIA
Taiwanese Journal of Mathematics, 2009Co-Authors: Lam Quoc Anh, Phan Quoc Khanh, Dang Thi My Van, Jen-chih YaoAbstract:We consider well-Posedness under perturbations of vector quasiequilibrium and bilevel-equilibrium problems. This kind of well-Posedness relates Hadamard and Tikhonov well-Posedness notions to sensitivity analysis and we apply largely techniques of the latter to establish sufficient conditions for wellPosedness under perturbations. We also propose several new semicontinuity and quasiconvexity notions to weaken the imposed assumptions. Our results are new or include as special cases recent existing results. Many examples are provided for the illustration purpose.
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Well-Posedness for Mixed Quasivariational-Like Inequalities
Journal of Optimization Theory and Applications, 2008Co-Authors: Lu-chuan Ceng, Nicolas Hadjisavvas, S. Schaible, Jen-chih YaoAbstract:In this paper, we introduce concepts of well-Posedness, and well-Posedness in the generalized sense, for mixed quasivariational-like inequalities where the underlying map is multivalued. We give necessary and sufficient conditions for the various kinds of well-Posedness to occur. Our results generalize and strengthen previously found results for variational and quasivariational inequalities.
