10.30495/ijm2c.2022.1938594.1230
A Method for Solving Nonsmooth Pseudoconvex Optimization
- Maryam Bala Seyed Ghasir*
1 - Aghileh Heydari1
- Mohammad Ali Badamchizadeh2
Received: 24-08-2021
Accepted: 20-01-2022
Published in Issue 30-03-2022
Copyright (c) 2024 International Journal of Mathematical Modeling & Computations
This work is licensed under a Creative Commons Attribution 4.0 International License.
Abstract
In this paper, a two layer recurrent neural network (RNN) is shown for solving nonsmooth pseudoconvex optimization . First it is proved that the equilibrium point of the proposed neural network (NN) is equivalent to the optimal solution of the orginal optimization problem. Then, it is proved that the state of the proposed neural network is stable in the sense of Lyapunov, and convergent to an exact optimal solution of the original optimization. Finally two examples are given to illustrate the effectiveness of the proposed neural network.
References
- W. Bian, L. Ma, S. Qin and X. Xue, Neural network for nonsmooth pseudoconvex optimization with
- general convex constraints, Neural Netw., 101 (2018) 1–14.
- L. Cheng, Z.-G. Hou, Y. Lin, M. Tan, W. C. Zhang and F.-X. Wu, Recurrent neural network for
- non-smooth convex optimization problems with application to the identification of geneic requlatory
- networks, IEEE Trans. Neural Netw., 22 (5) (2011) 714–726.
- L. Cheng, Z.-G. Hou and M. Tan, A delayed projection neural network for solving linear variational
- inequalities, IEEE Trans. Neural Netw., 20 (6) (2009), 915–925.
- M. J. Ebadi, A. Hosseini and M. M. Hosseini, A projection type stepest descent neural network for
- solving a class of nonsmooth optimization problems, Neurocomputing, 235 (26) (2017) 164–181.
- X. Hu and J. Wang, Solving pseudoconvex monotone variational inequalities and pseudoconvex
- optimization problems using the projection neural network, IEEE Trans. on Neural Netw., 17 (2006)
- –1499.
- X. Ju, C. Li, X. He and G. Feng, An inertial projection neural network for solving inverse variational
- inequalities, Neurocomputing, 406 (17) (2020) 99–105.
- Q. Li, Y. Liu and L. Zhu, Neural network for nonsmooth pseudoconvex optimization with general
- constraints, Neurocomputing, 131 (2014) 336–347.
- G. Li, Z. Yan and J. Wang, A one-layer recurrent neural network for constrained nonconvex optimization, Neural Netw., 61 (2014) 10–21.
- Q. Liu, Z. Guo and J. Wang, A one-layer recurrent neural network for constrained pseudoconvex
- optimization and its application for dynamic portfolio optimization, Neural Netw., 26 (2012) 99–109.
- Q. Liu and J. Wang, A one-layer recurrent neural network for constrained nonsmooth optimization,
- IEEE Trans. Syst. Man Cybern. Part B Cybern., 41 (5) (2011) 1323–1333.M. Bala Seyed Ghasir et al./ IJM2C, 12 - 01 (2022) 15-25. 25
- S. Qin, W. Bian and X. Xue, A new one-layer recurrent neural network for nonsmooth pseudoconvex
- optimization, Neurocomputing, 120 (2013) 655–662.
- S. Qin, D. Fan, P. Su and Q. Liu, A simplified recurrent neural network for pseudoconvex optimization
- subject to linear equality constraints, Commun. Nonlinear Sci. Numer. Simul., 19 (4)(2014) 789–798.
- S. Qin and X. Xue, A two-layer recurrent neural network for nonsmooth convex optimization problems, IEEE Trans. Neural Netw. Learn. Syst., 26 (6) (2015) 1149–1160.
- D. Tank and J. Hopfield, Simple neural optimization networks:and a/d neural convex signal decision
- circuit, IEEE Trans. Circuits Syst., 33 (1986) 533–554.
- Y. Xia and J. Wang, A recurrent neural network for nonlinear convex optimization subject to nonlinear inequality constraints, IEEE Trans. Circuits Syst., 51 (2004) 1385–1394.
- X. Xue and W. Bian, Subgradient-based neural networks for nonsmooth convex optimization problems, IEEE Trans. Circuits Syst. I Regul. Pap., 55 (8) (2008) 2378–2391.