Entropic proximal decomposition methods for convex programs and variational inequalities

Entropic proximal decomposition methods for convex programs and variational inequalities

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Article ID: iaor2003770
Country: Germany
Volume: 91
Issue: 1
Start Page Number: 33
End Page Number: 47
Publication Date: Jan 2001
Journal: Mathematical Programming
Authors: ,
Abstract:

We consider convex optimization and variational inequality problems with a given separable structure. We propose a new decomposition method for these problems which combines the recent logarithmic-quadratic proximal theory introduced by the authors with a decomposition method given by Chen-Teboulle for convex problems with particular structure. The resulting method allows to produce for the first time provably convergent decomposition schemes based on C Langrangians for solving convex structured problems. Under the only assumption that the primal–dual problems have nonempty solution sets, global convergence of the primal–dual sequence produced by the algorithm is established.

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