Sufficient optimality conditions and duality results for a bilevel multiobjective optimization problem via a Ψ reformulation. (2nd April 2020) - Gadhi, N.; Hamdaoui, K.; El idrissi, M.
ABSTRACT: 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.