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Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints

J. J. Ye and X. Y. Ye
Mathematics of Operations Research
Vol. 22, No. 4 (Nov., 1997), pp. 977-997
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/3690259
Page Count: 21
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Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints
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Abstract

In this paper we study optimization problems with variational inequality constraints in finite dimensional spaces. Kuhn-Tucker type necessary optimality conditions involving coderivatives are given under certain constraint qualifications including one that ensures nonexistence of nontrivial abnormal multipliers. The result is applied to bilevel programming problems to obtain Kuhn-Tucker type necessary optimality conditions. The Kuhn-Tucker type necessary optimality conditions are shown to be satisfied without any constraint qualification by the class of bilevel programming problems where the lower level is a parametric linear quadratic problem.

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