The so-called equilibrium problem is a mathematical model, which subsumes, among others, variational inequalities, noncooperative games, multi-objective and inverse optimization in a unified framework.
Descent methods exploit optimization reformulations of equilibrium problems (EPs) through appropriate gap functions. The talk aims at providing an overview of this class of methods. The basic ideas and features will be illustrated, in particular the role of monotonicity in overcoming the nonconvexities which come into play will be underlined. Afterwards, I will focus on some recent developments. First, I will show an algorithm for EPs with nonlinear constraints which involves only linearly constrained optimization problems: polyhedral approximations of the feasible region are exploited together with possibly unfeasible search directions, which call for exact penalties. Finally, I will show an algorithm which exploits pairs of gap functions in such a way that search directions can be exploited with no feasibility concern.
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