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Discontinuity, Nonlinearity, and Complexity 13(3) (2024) 399--409 | DOI:10.5890/DNC.2024.09.001

S. S. Chang$^1$, Salahuddin$^2$, L. Wang$^{3,4}$, D. P. Wu$^5$, Z. L. Ma$^{6,7}$

$^1$ Center for General Education, China Medical University, Taichung, 40402, Taiwan

$^2$ Department of Mathematics, Jazan University, Jazan-45142, Kingdom of Saudi Arabia

$^3$ Yunnan Key Laboratory of Service Computing, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China

$^4$ Institute of Intelligence Applications, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China

$^5$ Department of mathematics, Jinjiang College of Sichuan University, Pengshan, Sichuan, China

$^6$ College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China

$^7$ College of Public Foundation, Yunnan Open University (Yunnan Technical College of National Defence Industry), Kunming 650500, China

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Abstract

The main purpose of this paper is to study a class of non-stationary optimization problem whose objective function need not be smooth in general and only approximation sequences are known instead of exact values of the functions. In our article we presented a coordinate-wise descent splitting method for non-stationary decomposable composite optimization problem and proved convergence of the problems involving the non-smooth set-valued functions. In our paper we gave a general iterative method and proved an existence result of solution for the non-stationary generalized mixed variational inequality problems.

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