Geodesic
Strong-weak Stackelberg Problems in Finite Dimensional Spaces
Serdica Mathematical Journal, Tome 21 (1995) no. 2, pp. 151-170.

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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 results when the parameter ǫ goes to zero. Finally, as an example, we consider an optimization problem associated to a best bound given in [2] for a system of nondifferentiable convex inequalities.
Keywords: Marginal Functions, Two-Level Optimization, Limits of Sets, Stability, Convex Analysis 
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Aboussoror, Abdelmalek; Loridan, Pierre. Strong-weak Stackelberg Problems in Finite Dimensional Spaces. Serdica Mathematical Journal, Tome 21 (1995) no. 2, pp. 151-170. http://geodesic.mathdoc.fr/item/SMJ2_1995_21_2_a4/