Contributed Session Fri.1.MA 313

Friday, 10:30 - 12:00 h, Room: MA 313

Cluster 3: Complementarity & variational inequalities [...]

Algorithms for complementarity and related problems II


Chair: Goran Lesaja



Friday, 10:30 - 10:55 h, Room: MA 313, Talk 1

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

Coauthor: Giancarlo Bigi


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.



Friday, 11:00 - 11:25 h, Room: MA 313, Talk 2

Goran Lesaja
Infeasible full-Newton step interior-point method for linear complementarity problems


We present an infeasible Full-Newton-Step Interior-Point Method for Linear Complementarity Problems. The advantage of the method, in addition to starting from an infeasible starting point, is that it uses full Newton-steps, thus avoiding the calculation of the step size at each iteration. However, by suitable choice of parameters iterates are forced to stay in the neighborhood of the central path, thus, still guaranteeing the global convergence of the method. The number of iterations necessary to find epsilon-approximate solution of the problem matches the best known iteration bounds for these types of methods.


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