Strong-weak Stackelberg Problems in Finite Dimensional Spaces

Aboussoror, Abdelmalek, and Loridan, Pierre. "Strong-weak Stackelberg Problems in Finite Dimensional Spaces." Serdica Mathematical Journal 21.2 (1995): 151-170. <http://eudml.org/doc/11664>.

@article{Aboussoror1995,
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.},
author = {Aboussoror, Abdelmalek, Loridan, Pierre},
journal = {Serdica Mathematical Journal},
keywords = {Marginal Functions; Two-Level Optimization; Limits of Sets; Stability; Convex Analysis; two-level optimization; strong-weak Stackelberg problems; - approximate optimal solutions; system of nondifferentiable convex inequalities},
language = {eng},
number = {2},
pages = {151-170},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Strong-weak Stackelberg Problems in Finite Dimensional Spaces},
url = {http://eudml.org/doc/11664},
volume = {21},
year = {1995},
}

TY - JOUR
AU - Aboussoror, Abdelmalek
AU - Loridan, Pierre
TI - Strong-weak Stackelberg Problems in Finite Dimensional Spaces
JO - Serdica Mathematical Journal
PY - 1995
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 21
IS - 2
SP - 151
EP - 170
AB - 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.
LA - eng
KW - Marginal Functions; Two-Level Optimization; Limits of Sets; Stability; Convex Analysis; two-level optimization; strong-weak Stackelberg problems; - approximate optimal solutions; system of nondifferentiable convex inequalities
UR - http://eudml.org/doc/11664
ER -