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Gap functions for quasi-variational inequalities via duality [PDF]
Journal of Inequalities and Applications, 2018 This paper deals with an application of duality theory in optimization to the construction of gap functions for quasi-variational inequalities. The same approach was investigated for variational inequalities and equilibrium problems in (Pac. J. Optim.
L Altangerel
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Sensitivity Analysis in Variational Inequalities [PDF]
Mathematics of Operations Research, 1988 In this paper we derive conditions for the local uniqueness, continuity and differentiability of a solution of parametric variational inequalities. Our approach is new and has a strong geometric flavor. As an illustration we discuss the sensitivity of the classical complementarity problem.
Stella Dafermos
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Sensitivity Analysis for Variational Inequalities [PDF]
Mathematics of Operations Research, 1992 In this paper we study the behavior of the local solutions of perturbed variational inequalities, governed by perturbations to both the variational inequality function and the feasible region. Assuming appropriate second-order and regularity conditions, we show that the perturbed local solution set is Lipschitz continuous and directionally ...
Yuping Qiu, Thomas L. Magnanti
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Aggregative Variational Inequalities
Journal of Optimization Theory and Applications, 2023 AbstractWe enrich the theory of variational inequalities in the case of an aggregative structure by implementing recent results obtained by using the Selten–Szidarovszky technique. We derive existence, semi-uniqueness and uniqueness results for solutions and provide a computational method. As an application we derive very powerful practical equilibrium
von Mouche, Peter Hubert Mathieu +1 more
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Novel Algorithms for Solving a System of Absolute Value Variational Inequalities
Journal of Function Spaces, 2022 The goal of this paper is to study a new system of a class of variational inequalities termed as absolute value variational inequalities. Absolute value variational inequalities present a rational, pragmatic, and novel framework for investigating a wide ...
Safeera Batool +4 more
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Auxiliary Principle for Generalized Strongly Nonlinear Mixed Variational-Like Inequalities
Journal of Inequalities and Applications, 2009 We introduce and study a class of generalized strongly nonlinear mixed variational-like inequalities, which includes several classes of variational inequalities and variational-like inequalities as special cases.
Zeqing Liu +3 more
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Differential variational inequalities [PDF]
Mathematical Programming, 2007 This paper introduces and studies the class of differential variational inequalities (DVIs) in a finite-dimensional Euclidean space. The DVI provides a powerful modeling paradigm for many applied problems in which dynamics, inequalities, and discontinuities are present; examples of such problems include constrained time-dependent physical systems with ...
Jong-Shi Pang, David E. Stewart
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Fixed Point Theory and Applications, 2008 We introduce and study a new class of general nonlinear implicit variational inequalities, which includes several classes of variational inequalities and variational inclusions as special cases.
Jeong Sheok Ume +2 more
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On the Generalized Nonlinear Variational Inequalities and Quasi-Variational Inequalities
Journal of Mathematical Analysis and Applications, 1996 The paper deals with two kinds of variational inequality problems: 1. (Generalized nonlinear variational inequality problem -- GNVI\((T,g,b,X)\)) Find \(\widehat x\in X\) and \(\widehat w\in T\widehat x\) such that \[ \text{Re}\langle\widehat w,g(\widehat x) -g(y)\rangle+ b(\widehat x,\widehat x)- b(\widehat x,y)\geq 0\;\forall y\in X; \] 2 ...
Yu, Su-Jane, Yao, Jen-Chih
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Some Aspects of Extended General Variational Inequalities
Abstract and Applied Analysis, 2012 Noor (“Extended general variational inequalities,” 2009, “Auxiliary principle technique for extended general variational inequalities,” 2008, “Sensitivity analysis of extended general variational inequalities,” 2009, “Projection iterative methods for ...
Muhammad Aslam Noor
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