A proximal augmented Lagrangian method for equilibrium problems |
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Authors: | Javad Mashreghi |
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Institution: | Département de Mathématiques et de Statistique, Faculté des Sciences et de Génie , Université Laval , Québec, QC G1V 0A6, Canada |
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Abstract: | Considering a recently proposed proximal point method for equilibrium problems, we construct an augmented Lagrangian method for solving the same problem in reflexive Banach spaces with cone constraints generating a strongly convergent sequence to a certain solution of the problem. This is an inexact hybrid method meaning that at a certain iterate, a solution of an unconstrained equilibrium problem is found, allowing a proper error bound, followed by a Bregman projection of the initial iterate onto the intersection of two appropriate halfspaces. Assuming a set of reasonable hypotheses, we provide a full convergence analysis. |
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Keywords: | augmented Lagrangian method Bregman distance Bregman projection cone constraint equilibrium problem proximal point method |
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