Gap functions and penalization for solving equilibrium problems with nonlinear constraints |
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Authors: | Giancarlo Bigi Mauro Passacantando |
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Institution: | 1. Dipartimento di Informatica, Universit?? di Pisa, Largo B. Pontecorvo 3, 56127, Pisa, Italy 2. Dipartimento di Matematica Applicata, Universit?? di Pisa, via Buonarroti 1/c, 56127, Pisa, Italy
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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. |
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