Abstract
The main objects here are equilibrium problems of monotone type. Examples include convex minimization, convex-concave saddle problems, monotone variational inequalities, and many non-cooperative games. To solve such problems we propose a method using approximate subgradients, inexact orthogonal projections, and predetermined step sizes, the latter forming a divergent series. Our motivation stems in part from noncooperative games where the algorithm might depict an adaptive mode of repeated play. Granted existence of equilibria it is shown that the method generates a sequence which converges to such an outcome.
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© 1997 Springer-Verlag Berlin Heidelberg
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Flåm, S.D. (1997). Gradient Approaches to Equilibrium. In: Gritzmann, P., Horst, R., Sachs, E., Tichatschke, R. (eds) Recent Advances in Optimization. Lecture Notes in Economics and Mathematical Systems, vol 452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59073-3_4
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DOI: https://doi.org/10.1007/978-3-642-59073-3_4
Publisher Name: Springer, Berlin, Heidelberg
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