an:07181922
Zbl 1433.90151
Gadhi, N.; Hamdaoui, K.; El Idrissi, M.
Sufficient optimality conditions and duality results for a bilevel multiobjective optimization problem via a \(\Psi\) reformulation
EN
Optimization 69, No. 4, 681-702 (2020).
00448103
2020
j
90C29 90C46 49J52
bilevel programming; convexificator; duality; efficient solution; \( \Psi \)-function
Summary: In this paper, we are concerned with a bilevel multiobjective optimization problem \((P)\). Using the function \(\Psi\) introduced by the first author and \textit{S. Dempe} [J. Optim. Theory Appl. 155, No. 1, 100--114 (2012; Zbl 1267.90130)], 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 \textit{J. Dutta} and \textit{S. Chandra} [Optimization 53, No. 1, 77--94 (2004; Zbl 1079.90104)], we derive sufficient optimality conditions for the problem \((P)\) and establish Mond-Weir duality results. To illustrate the obtained results some examples are given.
Zbl 1267.90130; Zbl 1079.90104