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Equilibrium programming using proximal-like algorithms. (English) Zbl 0890.90150
Summary: We compute constrained equilibria satisfying an optimality condition. Important examples include convex programming, saddle problems, noncooperative games, and variational inequalities. Under a monotonicity hypothesis, we show that equilibrium solutions can be found via iterative convex minimization. In the main algorithm each stage of computation requires two proximal steps, possibly using Bregman functions. One step serves to predict the next point; the other helps to correct the new prediction. To enhance practical applicability we tolerate numerical errors.

MSC:
90C25Convex programming
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