A Globally Linearly Convergent Method for Pointwise Quadratically Supportable Convex-Concave Saddle Point Problems
| Autor: | Luke, D. Russell, Shefi, Ron |
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| Rok vydání: | 2017 |
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| Zdroj: | J. Math. Anal. Appl., 457(2):1568--1590, 2018 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jmaa.2017.02.068 |
| Popis: | We study the \emph{Proximal Alternating Predictor-Corrector} (PAPC) algorithm introduced recently by Drori, Sabach and Teboulle to solve nonsmooth structured convex-concave saddle point problems consisting of the sum of a smooth convex function, a finite collection of nonsmooth convex functions and bilinear terms. We introduce the notion of pointwise quadratic supportability, which is a relaxation of a standard strong convexity assumption and allows us to show that the primal sequence is R-linearly convergent to an optimal solution and the primal-dual sequence is globally Q-linearly convergent. We illustrate the proposed method on total variation denoising problems and on locally adaptive estimation in signal/image deconvolution and denoising with multiresolution statistical constraints. Comment: 34 pages, 18 figures |
| Databáze: | arXiv |
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