# Strong-weak Stackelberg Problems in Finite Dimensional Spaces

Aboussoror, Abdelmalek; Loridan, Pierre

Serdica Mathematical Journal (1995)

- Volume: 21, Issue: 2, page 151-170
- ISSN: 1310-6600

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topAboussoror, 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 -

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