Marginal Functions Two-Level Optimization Limits of Sets Stability Convex Analysis
Issue Date:
1995
Publisher:
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Serdica Mathematical Journal, Vol. 21, No 2, (1995), 151p-170p
Abstract:
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.