Optimality conditions for pessimistic semivectorial bilevel programming problems

Journal of inequalities and applications

Bingbing Liu¹ 

关键词: semivectorial bilevel programming;    multiobjective optimization;    weakly efficient solution;    bilevel optimal value function;    sensitivity analysis;    optimality condition;   

DOI  :  10.1186/1029-242X-2014-41

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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, 90C30, 90C31, 90C46.

【 授权许可】

CC BY