Gap functions and penalization for solving equilibrium problems with nonlinear constraints

Gap functions and penalization for solving equilibrium problems with nonlinear constraints

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Article ID: iaor20126384
Volume: 53
Issue: 2
Start Page Number: 323
End Page Number: 346
Publication Date: Oct 2012
Journal: Computational Optimization and Applications
Authors: ,
Keywords: programming: nonlinear
Abstract:

The paper deals with equilibrium problems (EPs) with nonlinear convex constraints. First, EP is reformulated as a global optimization problem introducing a class of gap functions, in which the feasible set of EP is replaced by a polyhedral approximation. Then, an algorithm is given for solving EP through a descent type procedure, which exploits also exact penalty functions, and its global convergence is proved. Finally, the algorithm is tested on a network oligopoly problem with nonlinear congestion constraints.

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