Equilibrium programming using proximal-like algorithms |
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Authors: | Sjur Didrik Flåm Anatoly S Antipin |
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Institution: | (1) Economics Department, Bergen University, 5007 Bergen, Norway;(2) Computing Centre, Russian Academy of Sciences, 117967 Moscow, Russia |
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Abstract: | 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.
Research supported partly by the Norwegian Research Council, project: Quantec 111039/401. |
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Keywords: | Equilibrium problems Convex programming Saddle problems Non-cooperative games Variational inequalities Quasi-monotonicity Proximal point algorithms Bregman distances |
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