期刊
SIAM JOURNAL ON OPTIMIZATION
卷 25, 期 2, 页码 1221-1248出版社
SIAM PUBLICATIONS
DOI: 10.1137/140971233
关键词
arbitrary sampling; block-coordinate algorithm; fixed-point algorithm; monotone operator splitting; primal-dual algorithm; stochastic quasi-Fejer sequence; stochastic algorithm; structured convex minimization problem
资金
- CNRS MASTODONS [2013MesureHD]
This work proposes block-coordinate fixed point algorithms with applications to nonlinear analysis and optimization in Hilbert spaces. The asymptotic analysis relies on a notion of stochastic quasi-Fejer monotonicity, which is thoroughly investigated. The iterative methods under consideration feature random sweeping rules to select arbitrarily the blocks of variables that are activated over the course of the iterations and they allow for stochastic errors in the evaluation of the operators. Algorithms using quasi-nonexpansive operators or compositions of averaged nonexpansive operators are constructed, and weak and strong convergence results are established for the sequences they generate. As a by-product, novel block-coordinate operator splitting methods are obtained for solving structured monotone inclusion and convex minimization problems. In particular, the proposed framework leads to random block-coordinate versions of the Douglas-Rachford and forward-backward algorithms and of some of their variants. In the standard case of m = 1 block, our results remain new as they incorporate stochastic perturbations.
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