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• W3121307036 abstract "Supported by the recent contributions in multiple domains, the first-order splitting became algorithms of choice for structured nonsmooth optimization. The large-scale noisy contexts make available stochastic information on the objective function and thus, the extension of proximal gradient schemes to stochastic oracles is heavily based on the tractability of the proximal operator corresponding to nonsmooth component, which has been highly exploited in the literature. However, some questions remained about the complexity of the composite models with proximal untractable terms. In this paper we tackle composite optimization problems, assuming only the access to stochastic information on both smooth and nonsmooth components, with a stochastic proximal first-order scheme with stochastic proximal updates. We provide sublinear $$mathcal {O}left( frac{1}{k} right) $$ convergence rates (in expectation of squared distance to the optimal set) under the strong convexity assumption on the objective function. Also, linear convergence is achieved for convex feasibility problems. The empirical behavior is illustrated by numerical tests on parametric sparse representation models." @default.
• W3121307036 created "2021-02-01" @default.
• W3121307036 creator A5049988389 @default.
• W3121307036 creator A5055191887 @default.
• W3121307036 date "2021-01-25" @default.
• W3121307036 modified "2023-09-24" @default.
• W3121307036 title "Stochastic proximal splitting algorithm for composite minimization" @default.
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• W3121307036 doi "https://doi.org/10.1007/s11590-021-01702-7" @default.
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