Global efficiency for multiobjective bilevel programming problems under generalized invexity
This paper deals with a nonlinear bilevel programming problem (problem NB). At the upper level, a vector optimization problem is considered while at the lower level, a scalar optimization problem arises. After giving some preliminaries and definitions, in Section 3 the KKT-conditions for the lower-level problem are used to reformulate the problem as a multi-objective single-level programming problem with equality and inequality constraints (problem MS). Sections 4 and 5 present necessary and sufficient efficiency conditions. The core of Section 4 is a Fritz John type necessary efficiency condition for problem NB. In Section 5, Fritz John type sufficient efficient conditions for a feasible point to be weakly efficient (Section 5.1), efficient (Section 5.2) and properly efficient (Section 5.3) for problem MS are given under different forms of generalized invexity and infineness. In Section 6, the case is studied where the optimization problems at both levels are linear. Two examples are discussed to illustrate the results obtained in this paper.
necessary and sufficient efficiency conditions
scientific article; zbMATH DE number 6692498
scientific article