A note on complementarity problem.
Carbone, Antonio (1998)
International Journal of Mathematics and Mathematical Sciences
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Carbone, Antonio (1998)
International Journal of Mathematics and Mathematical Sciences
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Giovanni P. Crespi, Ivan Ginchev, Matteo Rocca (2005)
RAIRO - Operations Research - Recherche Opérationnelle
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The existence of solutions to a scalar Minty variational inequality of differential type is usually related to monotonicity property of the primitive function. On the other hand, solutions of the variational inequality are global minimizers for the primitive function. The present paper generalizes these results to vector variational inequalities putting the Increasing Along Rays (IAR) property into the center of the discussion. To achieve that infinite elements in the image space are...
Plubtieng, Somyot, Sombut, Kamonrat (2010)
Journal of Inequalities and Applications [electronic only]
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Ching-Yan Lin, Liang-Ju Chu (2003)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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In this paper, a general existence theorem on the generalized variational inequality problem GVI(T,C,ϕ) is derived by using our new versions of Nikaidô's coincidence theorem, for the case where the region C is noncompact and nonconvex, but merely is a nearly convex set. Equipped with a kind of V₀-Karamardian condition, this general existence theorem contains some existing ones as special cases. Based on a Saigal condition, we also modify the main theorem to obtain another existence theorem...
Peng, Jian-Wen, Yang, Xin-Min (2006)
Journal of Inequalities and Applications [electronic only]
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Park, Sehie, Chen, Ming-Po (1998)
Journal of Inequalities and Applications [electronic only]
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F. Giannessi, G. Matroeni, X. Q. Yang (2009)
Bollettino dell'Unione Matematica Italiana
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The paper consists in a brief overview on Vector Variational Inequalities (VVI). The connections between VVI and Vector Optimization Problems (VOP) are considered. This leads to point out that necessary optimality conditions for a VOP can be formulated by means of a VVI when the objective function is Gâteaux differentiable and the feasible set is convex. In particular, the existence of solutions and gap functions associated with VVI are analysed. Gap functions provide an equivalent formulation...
Addou, A., Mermri, E.B. (2001)
International Journal of Mathematics and Mathematical Sciences
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Ceng, Lu-Chuan, Guu, Sy-Ming, Yao, Jen-Chih (2007)
Journal of Inequalities and Applications [electronic only]
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Giannessi, F. (1997)
Journal of Inequalities and Applications [electronic only]
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Alexander Kaplan, Rainer Tichatschke (2007)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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Interior proximal methods for variational inequalities are, in fact, designed to handle problems on polyhedral convex sets or balls, only. Using a slightly modified concept of Bregman functions, we suggest an interior proximal method for solving variational inequalities (with maximal monotone operators) on convex, in general non-polyhedral sets, including in particular the case in which the set is described by a system of linear as well as strictly convex constraints. The convergence...
Xiang, Fangni, Debnath, Lokenath (1996)
International Journal of Mathematics and Mathematical Sciences
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Lemaire, B. (1996)
Journal of Convex Analysis
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Li, Xi, Kim, Jong Kyu, Huang, Nan-Jing (2010)
Journal of Inequalities and Applications [electronic only]
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