Convergence analysis of the stochastic reflected forward–backward splitting algorithm

We propose and analyze the convergence of a novel stochastic algorithm for solving monotone inclusions that are the sum of a maximal monotone operator and a monotone, Lipschitzian operator. The propose algorithm requires only unbiased estimations of the Lipschitzian operator. We obtain the rate O (...

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Vydáno v:Optimization letters Ročník 16; číslo 9; s. 2649 - 2679
Hlavní autoři: Nguyen, Van Dung, Vũ, Bắng Công
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2022
Témata:
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
Monotone inclusion
Duality
Stochastic optimization
Reflected method
Ergodic convergence
Primal–dual algorithm
ISSN:1862-4472, 1862-4480
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Popis
Shrnutí:We propose and analyze the convergence of a novel stochastic algorithm for solving monotone inclusions that are the sum of a maximal monotone operator and a monotone, Lipschitzian operator. The propose algorithm requires only unbiased estimations of the Lipschitzian operator. We obtain the rate O ( l o g ( n ) / n ) in expectation for the strongly monotone case, as well as almost sure convergence for the general case. Furthermore, in the context of application to convex–concave saddle point problems, we derive the rate of the primal–dual gap. In particular, we also obtain O ( 1 / n ) rate convergence of the primal–dual gap in the deterministic setting.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-021-01844-8