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Article Dans Une Revue Computational Optimization and Applications Année : 2015

Mirror Prox Algorithm for Multi-Term Composite Minimization and Semi-Separable Problems

Résumé

In the paper, we develop a composite version of Mirror Prox algorithm for solving convexconcavesaddle point problems and monotone variational inequalities of special structure, allowingto cover saddle point/variational analogies of what is usually called “composite minimization”(minimizing a sum of an easy-to-handle nonsmooth and a general-type smooth convex functions“as if” there were no nonsmooth component at all). We demonstrate that the composite MirrorProx inherits the favourable (and unimprovable already in the large-scale bilinear saddle pointcase) O(1/ε) efficiency estimate of its prototype. We demonstrate that the proposed approach canbe successfully applied to Lasso-type problems with several penalizing terms (e.g. acting togetherl1 and nuclear norm regularization) and to problems of semi-separable structures considered inthe alternating directions methods, implying in both cases methods with the O(1/ε) complexitybounds.
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Dates et versions

hal-01335905 , version 1 (04-09-2024)

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Niao He, Anatoli B. Juditsky, Arkadii S. Nemirovskii. Mirror Prox Algorithm for Multi-Term Composite Minimization and Semi-Separable Problems. Computational Optimization and Applications, 2015, 61 (2), pp.275-319. ⟨10.1007/s10589-014-9723-3⟩. ⟨hal-01335905⟩
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