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Optimality conditions for pessimistic semivectorial bilevel programming problems. (English) Zbl 1332.90212
Summary: In this paper, a class of pessimistic semivectorial bilevel programming problems is investigated. By using the scalarization method, we transform the pessimistic semivectorial bilevel programming problem into a scalar objective optimization problem with inequality constraints. Furthermore, we derive a generalized minimax optimization problem using the maximization bilevel optimal value function, of which the sensitivity analysis is constructed via the lower-level value function approach. Using the generalized differentiation calculus of Mordukhovich, the first-order necessary optimality conditions are established in the smooth setting. As an application, we take the optimality conditions of the bilevel programming problems with multiobjective lower level problem when the lower level multiobjective optimization problem is linear with respect to the lower-level variables.

MSC:
90C26 Nonconvex programming, global optimization
90C30 Nonlinear programming
90C31 Sensitivity, stability, parametric optimization
90C46 Optimality conditions and duality in mathematical programming
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