Solution Concepts and New Optimality Conditions in Bilevel Multiobjective Programming

Affiliation(s)

Department of Mathematics, Faculty of Science, University of Yaoundé I, Yaoundé, Cameroon.

Department of Computer Sciences, Faculty of Science, University of Yaoundé I, Yaoundé, Cameroon.

Regional Bureau for Education in Africa, Pole de Dakar, UNESCO, Dakar, Senegal.

Department of Mathematics, Faculty of Science, University of Yaoundé I, Yaoundé, Cameroon.

Department of Computer Sciences, Faculty of Science, University of Yaoundé I, Yaoundé, Cameroon.

Regional Bureau for Education in Africa, Pole de Dakar, UNESCO, Dakar, Senegal.

Abstract

In this paper, new sufficient optimality theorems for a solution of a differentiable bilevel multiobjective optimization problem (BMOP) are established. We start with a discussion on solution concepts in bilevel multiobjective programming; a theorem giving necessary and sufficient conditions for a decision vector to be called a solution of the BMOP and a proposition giving the relations between four types of solutions of a BMOP are presented and proved. Then, under the pseudoconvexity assumptions on the upper and lower level objective functions and the quasiconvexity assumptions on the constraints functions, we establish and prove two new sufficient optimality theorems for a solution of a general BMOP with coupled upper level constraints. Two corollary of these theorems, in the case where the upper and lower level objectives and constraints functions are convex are presented.

In this paper, new sufficient optimality theorems for a solution of a differentiable bilevel multiobjective optimization problem (BMOP) are established. We start with a discussion on solution concepts in bilevel multiobjective programming; a theorem giving necessary and sufficient conditions for a decision vector to be called a solution of the BMOP and a proposition giving the relations between four types of solutions of a BMOP are presented and proved. Then, under the pseudoconvexity assumptions on the upper and lower level objective functions and the quasiconvexity assumptions on the constraints functions, we establish and prove two new sufficient optimality theorems for a solution of a general BMOP with coupled upper level constraints. Two corollary of these theorems, in the case where the upper and lower level objectives and constraints functions are convex are presented.

Cite this paper

F. Dedzo, L. Fotso and C. Pieume, "Solution Concepts and New Optimality Conditions in Bilevel Multiobjective Programming,"*Applied Mathematics*, Vol. 3 No. 10, 2012, pp. 1395-1402. doi: 10.4236/am.2012.330196.

F. Dedzo, L. Fotso and C. Pieume, "Solution Concepts and New Optimality Conditions in Bilevel Multiobjective Programming,"

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