Well-Posedness by Perturbations of Variational Problems

Lemaire, B.; Salem, C. Ould Ahmed; Revalski, Julian P.

doi:10.1023/a:1020840322436

Cited by 39 publications

(22 citation statements)

References 17 publications

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“…Since then many kinds of well-posedness concepts and applications in game theory and vector optimization problems were studied (see [2]). Extensions of well-posedness to other related problems, such as fixed point problems (see [14]), variational inequality problems (see [15]) and bilevel optimization problems (see [19]), were considered. Recently, Lignola and Morgan [15] studied well-posedness for a class of mathematical program…”

mentioning

confidence: 99%

Well-posedness for parametric vector equilibrium problems with applications

Kimura¹,

Liou²,

Wu³

et al. 2008

Journal of Industrial &Amp; Management Optimization

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Abstract. In this paper, we study the parametric well-posedness for vector equilibrium problems and propose a generalized well-posed concept for equilibrium problems with equilibrium constraints (EPEC in short) in topological vector spaces setting. We show that under suitable conditions, the well-posedness defined by approximating solution nets is equivalent to the upper semicontinuity of the solution mapping of perturbed problems. Further, since optimization problems and variational inequality problems are special cases of equilibrium problems, related variational problems can be adopted under some equivalent conditions. Finally, we also study the relationship between well-posedness and parametric well-posedness.1. Introduction. The concept of well-posedness is closely related to stability, approximation and numerical analysis. An initial concept of well-posedness introduced by Tykhonov, was given in scalar optimization (see [4]). Since then many kinds of well-posedness concepts and applications in game theory and vector optimization problems were studied (see [2]). Extensions of well-posedness to other related problems, such as fixed point problems (see [14]), variational inequality problems (see [15]) and bilevel optimization problems (see [19]), were considered. Recently, Lignola and Morgan [15] studied well-posedness for a class of mathematical program

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mentioning

confidence: 99%

Well-posedness for parametric vector equilibrium problems with applications

Kimura¹,

Liou²,

Wu³

et al. 2008

Journal of Industrial &Amp; Management Optimization

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“…The concept of well-posedness has been generalized to some other problems: variational inequality problems [5,6,9,10,13,16,19,29], saddle point problems [4], Nash equilibrium problems [20,21], inclusion problems [9,15], and fixed point problems [9,15,22].…”

Section: Introductionmentioning

confidence: 99%

Well-posedness for systems of generalized mixed quasivariational inclusion problems and optimization problems with constraints

Ceng¹,

Liou²,

Yao³

et al. 2017

J. Nonlinear Sci. Appl.

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In this paper, several metric characterizations of well-posedness for systems of generalized mixed quasivariational inclusion problems and for optimization problems with systems of generalized mixed quasivariational inclusion problems as constraints are given. The equivalence between the well-posedness of systems of generalized mixed quasivariational inclusion problems and the existence of solutions of systems of generalized mixed quasivariational inclusion problems is given under suitable conditions.

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“…In recent years, the concept of well-posedness has been generalized to several related problems: variational inequality problems [14][15][16][17][18], saddle point problems [19], Nash equilibrium problems [16,[20][21][22][23], inclusion problems [24,25], and fixed point problems [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Well-posedness for parametric strong vector quasi-equilibrium problems with applications

Wang

2011

Fixed Point Theory Appl

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In this article, we generalize the concept of well-posedness to the parametric strong vector quasi-equilibrium problem. Under some suitable conditions, we establish some characterizations of well-posedness for parametric strong vector quasiequilibrium problems. The corresponding concept of well-posedness in the generalized sense is also investigated for the parametric strong vector quasiequilibrium problem. As applications, we investigate the well-posedness for strong vector quasi-variational inequality problems and strong vector quasi-optimization problems. 2000 Mathematics subject classification: 49K40; 90C31.

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Well-Posedness by Perturbations of Variational Problems

Cited by 39 publications

References 17 publications

Well-posedness for parametric vector equilibrium problems with applications

Well-posedness for parametric vector equilibrium problems with applications

Well-posedness for systems of generalized mixed quasivariational inclusion problems and optimization problems with constraints

Well-posedness for parametric strong vector quasi-equilibrium problems with applications

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