Constraint Qualifications and Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints
Jane J. Ye · SIAM Journal on Optimization · 2000
A very general optimization problem with a variational inequality constraint, inequality constraints, and an abstract constraint are studied. Fritz John type and Kuhn--Tucker type necessary optimality conditions involving Mordukhovich coderivatives are derived. Several constraint qualifications for the Kuhn--Tucker type necessary optimality conditions involving Mordukhovich coderivatives are introduced and their relationships are studied. Applications to bilevel programming problems are also given.