Friday, 10:30 - 10:55 h, Room: MA 313

 

Mauro Passacantando
Gap functions and penalization for solving equilibrium problems with nonlinear constraints

Coauthor: Giancarlo Bigi

 

Abstract:
Several descent methods for solving equilibrium problems (EPs) have been recently proposed. They are based on the reformulation of EP as a global optimization problem through gap functions. Most approaches need to minimize a convex function over the feasible region in order to evaluate the gap function, and such evaluation may be computationally expensive when the feasible region is described by nonlinear convex inequalities. In this talk we introduce a new family of gap functions which rely on a polyhedral approximation of the feasible region rather than on the feasible region itself. We analyze some continuity and generalized differentiability properties and we prove that monotonicity type assumptions guarantee that each stationary point of a gap function is actually a solution of EP. Finally, we proposed two descent algorithms for solving EPs. Unlike most of the available algorithms, we consider a search direction which could be unfeasible, so that the use of an exact penalty function is required. The two algorithms differ both for the updating of regularization and penalization parameters and for the assumptions which guarantee their global convergence.

 

Talk 1 of the contributed session Fri.1.MA 313
"Algorithms for complementarity and related problems II" [...]
Cluster 3
"Complementarity & variational inequalities" [...]

 

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