A dual-based stochastic inexact algorithm for a class of stochastic nonsmooth convex composite problems

Gui-Hua Lin (), Zhen-Ping Yang (), Hai-An Yin () and Jin Zhang ()
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Gui-Hua Lin: Shanghai University
Zhen-Ping Yang: Jiaying University
Hai-An Yin: Southern University of Science and Technology
Jin Zhang: Peng Cheng Laboratory

Computational Optimization and Applications, 2023, vol. 86, issue 2, No 8, 669-710

Abstract: Abstract In this paper, a dual-based stochastic inexact algorithm is developed to solve a class of stochastic nonsmooth convex problems with underlying structure. This algorithm can be regarded as an integration of a deterministic augmented Lagrangian method and some stochastic approximation techniques. By utilizing the sparsity of the second order information, each subproblem is efficiently solved by a superlinearly convergent semismooth Newton method. We derive some almost surely convergence properties and convergence rate of objective values. Furthermore, we present some results related to convergence rate of distance between iteration points and solution set under error bound conditions. Numerical results demonstrate favorable comparison of the proposed algorithm with some existing methods.

Keywords: Stochastic programming; Stochastic approximation; Duality; Convergence rate; 90C06; 90C15; 90C25 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10589-023-00504-0

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