Gap functions and penalization for solving equilibrium problems with nonlinear constraints

Authors:
Giancarlo Bigi;Mauro Passacantando
Affiliations:
Dipartimento di Informatica, Università di Pisa, Pisa, Italy 56127;Dipartimento di Matematica Applicata, Università di Pisa, Pisa, Italy 56127
Venue:
Computational Optimization and Applications
Year:
2012

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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.