The steepest descent direction for the nonlinear bilevel programming problem

Authors:
Gilles Savard;Jacques Gauvin
Affiliations:
Gerad. École Polytechnique de Montréal, Département de mathématiques appliquées, C.P. 6079, Succ. Centre-Ville, Montréal Québec, Canada, H3C 3A7;École Polytechnique de Montréal, Département de mathématiques appliquées, C.P. 6079, Succ. Centre-Ville, Montréal Québec, Canada, H3C 3A7
Venue:
Operations Research Letters
Year:
1994

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Abstract

In this paper, we give necessary optimality conditions for the nonlinear bilevel programming problem. Furthermore, at each feasible point, we show that the steepest descent direction is obtained by solving a quadratic bilevel programming problem. We give indication that this direction can be used to develop a descent algorithm for the nonlinear bilevel problem.