Interior proximal methods for equilibrium programming: part I
Nils Langenberg · Optimization · 2011
In this article a method for solving equilibrium problems introduced by Flåm and Antipin [S.D. Flåm and A.S. Antipin, Equilibrium programming using proximal-like algorithms, Math. Program. 77 (1997), pp. 29–41] is discussed. We extend this method to unbounded feasible sets which also leads to the necessity of a new discussion of solvability of the subproblems and appropriate stopping criteria. We also provide results permitting the use of zone-coercive regularizing functionals (of Bregman type). For example, when the boundary of the feasible set has a certain curvature, the regularized subproblems can be treated as unconstrained ones.