Sufficient optimality conditions and duality results for a bilevel multiobjective optimization problem via a psi reformulation

摘要

In this paper, we are concerned with a bilevel multiobjective optimization problem . Using the function psi introduced by Gadhi and Dempe [Necessary optimality conditions and a new approach to multiobjective bilevel optimization problems. J Optim Theory Appl. 2012;155:100-114], we reformulate as a single level mathematical programming problem and establish/exhibit the global equivalence between the two problems and . Using a generalized convexity introduced by Dutta and Chandra [Convexificator, generalized convexity and vector optimization. Optimization. 2004;53:77-94], we derive sufficient optimality conditions for the problem and establish Mond-Weir duality results. To illustrate the obtained results some examples are given.