Sufficient optimality conditions and duality results for a bilevel multiobjective optimization problem via a Ψ reformulation
Nazih Abderrazzak Gadhi, Khadija Hamdaoui, Mohammed El Idrissi · Optimization · 2019
In this paper, we are concerned with a bilevel multiobjective optimization problem P. Using the function Ψ 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 P as a single level mathematical programming problem P∗ and establish/exhibit the global equivalence between the two problems P and P∗. 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 P and establish Mond-Weir duality results. To illustrate the obtained results some examples are given.