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Strong-weak Stackelberg Problems in Finite Dimensional Spaces

Aboussoror, AbdelmalekLoridan, Pierre — 1995

Serdica Mathematical Journal

We are concerned with two-level optimization problems called strongweak Stackelberg problems, generalizing the class of Stackelberg problems in the strong and weak sense. In order to handle the fact that the considered two-level optimization problems may fail to have a solution under mild assumptions, we consider a regularization involving ε-approximate optimal solutions in the lower level problems. We prove the existence of optimal solutions for such regularized problems and present some approximation...

Existence of solutions to weak nonlinear bilevel problems MinSup and d.c. problems

Abdelmalek AboussororAbdelatif Mansouri — 2008

RAIRO - Operations Research

In this paper, which is an extension of [4], we first show the existence of solutions to a class of Min Sup problems with linked constraints, which satisfy a certain property. Then, we apply our result to a class of weak nonlinear bilevel problems. Furthermore, for such a class of bilevel problems, we give a relationship with appropriate d.c. problems concerning the existence of solutions.

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