On the Gap Functions of Prevariational Inequalities

X.Q. Yang
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X.Q. Yang: Hong Kong Polytechnic University

Journal of Optimization Theory and Applications, 2003, vol. 116, issue 2, No 12, 437-452

Abstract: Abstract Gap functions play a crucial role in transforming a variational inequality problem into an optimization problem. Then, methods solving an optimization problem can be exploited for finding a solution of a variational inequality problem. It is known that the so-called prevariational inequality is closely related to some generalized convex functions, such as linear fractional functions. In this paper, gap functions for several kinds of prevariational inequalities are investigated. More specifically, prevariational inequalities, extended prevariational inequalities, and extended weak vector prevariational inequalities are considered. Furthermore, a class of gap functions for inequality constrained prevariational inequalities is investigated via a nonlinear Lagrangian.

Keywords: Variational inequalities; gap functions; Lagrangian functions; linear fractional functions (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1023/A:1022422407705

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