The Study of Coordinate-Wise Decomposition Descent Method for Non-Stationary Optimization Problems

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Authors

  • S. S. Chang Center for General Education, China Medical University, Taichung, 40402, Taiwan Author
  • Salahuddin Department of Mathematics, Jazan University, Jazan-45142, Kingdom of Saudi Arabia Author
  • L. Wang Yunnan Key Laboratory of Service Computing, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China; Institute of Intelligence Applications, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China Author
  • D. P. Wu Department of mathematics, Jinjiang College of Sichuan University, Pengshan, Sichuan, China Author
  • Z. L. Ma College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China; College of Public Foundation, Yunnan Open University (Yunnan Technical College of National Defence Industry), Kunming 650500, China Author

DOI:

https://doi.org/10.5890/DNC.2024.09.001

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.

References

[1] Stampacchia, G. (1968), "Variational Inequalities", in: Theory and Applications of Monotone Operators, Proceedings of the NATO Advanced Study Institute, Venice, Italy (Edizioni Odersi, Gubbio, Italy) pp. 1020192.

[2] Sofonea, M., Han, W., and Migorski, S. (2015), Numerical analysis of history-dependent variational inequalities with applications to contact problems, European Journal of Applied Mathematics, 26, 427-452.

[3] Hintermuller, M. (2001), Inverse coefficient problems for variational inequalities, optimality conditions and numerical realization, ESAIM: Mathematical Modelling and Numerical Analysis, 35, 129-152.

[4] Salahuddin (2020), A coordinate wise variational method with tolerance functions, Journal of Applied Nonlinear Dynamics, 9(4), 541-549.

[5] Konnov, I.V. (2014), Right-hand side decomposition for variational inequalities, Journal of Optimization Theory and Applications, 160, 221-238.

[6] Cevher, V., Becker, S., and Schmidt, M. (2014), Convex optimization for big data, Signal Process Magazine, 31, 32-43.

[7] Facchinei, F., Scutari, G., and Sagratella, S. (2015),Parallel selective algorithms for non convex big data optimization, IEEE Transactions on Signal Processing, 63, 1874-1889.

[8] Konnov, I.V. (2017), Decomposition descent method for limit optimization problems, In Learning and Intelligent Optimization: 11th International Conference, LION 11, Nizhny Novgorod, Russia, 166-179. doi.org/10.1007/978-3-319-69404-7-12.

[9] Konnov, I.V. (2019), Selective bi-coordinate method for limit non-smooth resource allocation type problems, Set-Valued and Variational Analysis, 27(1), 191-211. DOI10.1007/s11228-017-0447-2.

[10] Tseng, P. and Yun, S. (2010), A coordinate gradient descent method for nonsmooth separable minimization, Mathematical Programming, 117, 387-423.

[11] Konnov, I.V. and Salahuddin, (2017), Two-level iterative method for non-stationary mixed variational inequalities, Russian Mathematics, 61(10), 44-53.

[12] Salahuddin (2020), Iterative method for non-stationary mixed variational inequalities, Discontinuity, Nonlinearity, and Complexity, 9(4), 647-655.

[13] Clarke, F.H. (1983), Optimization and Nonsmooth Analysis, Wiley, New york.

[14] Konnov, I.V. (2015), Sequential threshold control in descent splitting methods for decomposable optimization problems, Optimization Methods and Software, 30(4), 1238-1254.

[15] Ermoliev, Y.M., Norkin, V.I., and Wets, R.J.B. (1995), The minimization of semicontinuous functions: mollifier subgradient, Siam Journal on Control and Optimization, 33(1), 149-167.

[16] Czarnecki, M.O. and Rifford, L. (2006), Approximation and regularization of Lipschitz functions: convergence of the gradients, Transactions of the American Mathematical Society, 358, 4467-4520.

[17] Engl, H.W., Hanke, M., and Neubauer, A. (1996), Regularization of Inverse Problems, Kluwer Acad. Pub., Dordrecht.

[18] Tibshirani, R. (1996), Regression shrinkage and selection via the lasso, Journal of the Royal Statistical Society Series B: Statistical Methodology, 58, 267-288.

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PublishedSeptember 2024

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How to Cite

Chang, S. S., Salahuddin, Wang, L., Wu, D. P., & Ma, Z. L. (2026). The Study of Coordinate-Wise Decomposition Descent Method for Non-Stationary Optimization Problems. Discontinuity, Nonlinearity, and Complexity, 13(3), 399-409. https://doi.org/10.5890/DNC.2024.09.001