Constraint Qualifications and Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints

Jane Ye
University of Victoria/Mathematics and Statistics
janeye@uvic.ca

ABSTRACT. An optimization problem with variational inequality constraints (OPVIC) is a very general optimization problem where constraints may include inequality constraints, an abstract constraint and a variational inequality constraint. In this talk, we present a very general first order theory for (OPVIC). We derive both Fritz John type and Kuhn-Tucker type necessary optimality conditions involving Mordukhovich coderivatives, introduce several constraint qualifications for the Kuhn-Tucker type necessary optimality conditions involving Mordukhovich coderivatives and study their relationships. We will also illustrate the theory by applying it to the bilevel programming problems.

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