A method of solving a class of Bilevel fractional/quadratic programming problem

Session : PM / Programmation Mathématique
Nacera Maachou et Mustapha Moulaï

In this paper, a class of bilevel optimization problems has been considered where Bilevel Quadratic Fractional Programming problem has an additional characteristic, i.e A method of solving Bilevel quadratic fractional/quadratic problem in which the leader's objective is quadratic fractional and the follower's objective is quadratic. The variables associated with both the level problems are related by linear constraints. The purpose of this paper is to find the optimality conditions and a solution procedure to solve it, the algorithm is based on Karush-Kuhn-Tucker conditions and a related bilevel linear fractional-quadratic problem is constructed in which the leader's objective is linear fractional and the follower's objective is quadratic in order to obtain an optimal solution of a bilevel quadratic fractional-quadratic programming problem. The main idea behind our method is to scan the extreme points (basic feasible solutions) of the related bilevel linear fractional- quadratic programming problem in a systematic manner till an optimal solution of the problem is obtained.

Mots clés : Extreme point, Bilevel Programming, Karush-Kuhn-Tucker conditions