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 ∞ Lagrangians for solving convex structured problems. Under the only assumption that the primal-dual problems have nonempty solution sets, global convergence of the primal-dual sequences produced by the algorithm is established.
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Received: October 6, 1999 / Accepted: February 2001¶Published online September 17, 2001
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Auslender, A., Teboulle, M. Entropic proximal decomposition methods for convex programs and variational inequalities. Math. Program. 91, 33–47 (2001). https://doi.org/10.1007/s101070100241
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DOI: https://doi.org/10.1007/s101070100241