Multiobjective Optimization Problem with Variational Inequality Constraintst

J. J. Ye and Q. J. Zhu

Abstract: We study a general multiobjective optimization problem with variational inequality, equality,
inequality and abstract constraints. Fritz John type necessary optimality conditions involving Mordukhovich
coderivatives are derived. They lead to Kuhn-Tucker type necessary optimality conditions under additional constraint qualifications including the calmness condition, the error bounded constraint qualification, the no nonzero abnormal multiplier constraint qualification, the generalized Mangasarian-Fromovitz condition, the strongly regular constraint qualification and the
linear constraint qualification. We then apply these results to the multiobjective optimization problem with complementary constraints and the multiobjective bilevel programming problem.


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