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

Lin, Gui-Hua1; Yang, Zhen-Ping2; Yin, Hai-An3; Zhang, Jin4

2023-07-01

10.1007/s10589-023-00504-0

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS   影响因子和分区

0926-6003

1573-2894

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.

Stochastic programming Stochastic approximation Duality Convergence rate

SCI ; EI

英语

通讯

Operations Research & Management Science ; Mathematics

Operations Research & Management Science ; Mathematics, Applied

WOS:001028904100001

SPRINGER

20232914413615

Approximation algorithms ; Approximation theory ; Constrained optimization ; Lagrange multipliers ; Newton-Raphson method ; Numerical methods ; Stochastic systems

Control Systems:731.1 ; Mathematics:921 ; Numerical Methods:921.6 ; Systems Science:961

ENGINEERING

Web of Science

1.Shanghai Univ, Sch Management, Shanghai 200444, Peoples R China
2.Jiaying Univ, Sch Math, Meizhou 514015, Peoples R China
3.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China
4.Southern Univ Sci & Technol, SUSTech Int Ctr Math, Natl Ctr Appl Math Shenzhen, Dept Math,Peng Cheng Lab, Shenzhen 518055, Peoples R China

Lin, Gui-Hua,Yang, Zhen-Ping,Yin, Hai-An,et al. A dual-based stochastic inexact algorithm for a class of stochastic nonsmooth convex composite problems[J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,2023,86(2):669-710.

Lin, Gui-Hua,Yang, Zhen-Ping,Yin, Hai-An,&Zhang, Jin.(2023).A dual-based stochastic inexact algorithm for a class of stochastic nonsmooth convex composite problems.COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,86(2),669-710.

Lin, Gui-Hua,et al."A dual-based stochastic inexact algorithm for a class of stochastic nonsmooth convex composite problems".COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 86.2(2023):669-710.