Quasi-variational equilibrium models for network flow problems

We consider a formulation of a network equilibrium problem given by a suitable quasi-variational inequality where the feasible flows are supposed to be dependent on the equilibrium solution of the model. The Karushâ\u80\u93Kuhnâ\u80\u93Tucker optimality conditions for this quasi-variational inequality allow us to consider dual variables, associated with the constraints of the feasible set, which may receive interesting interpretations in terms of the network, extending the classic ones existing in the literature

Descent and penalization techniques for equilibrium problems with nonlinear constraints

This paper deals with equilibrium problems with nonlinear constraints. Exploiting a gap function recently introduced, which rely on a polyhedral approximation of the feasible region, we propose two descent methods. They are both based on the minimization of a suitable exact penalty function, but they use different rules for updating the penalization parameter and they rely on different types of line search. The convergence of both algorithms is proved under standard assumptions

Gap functions and penalization for solving equilibrium problems with nonlinear constraints

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 related to exact penalties of the gap functions and its global convergence is proved. Finally, the algorithm is tested on a network oligopoly problem with nonlinear congestion constraints<br /

Error Tolerant Descent Methods for Computing Equilibria

Equilibrium problems naturally arise in the modelling of competitive agents systems in many fields of Engineering. Several descent methods have been developed to solve them, usually asking for an exact solution of auxiliary optimization problems at each step. We propose two algorithms that rely only on approximated solutions of these auxiliary problems. Some ideas on possible methods for computing these solutions efficiently controlling the error are also given. Preliminary numerical tests on cloud computing scenarios have been carried out