A New Steepest Descent Differential Inclusion-Based Method for Solving General Nonsmooth Convex Optimization Problems
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In this paper, we investigate a steepest descent neural network for solving general nonsmooth convex optimization problems. The convergence to optimal solution set is analytically proved. We apply the method to some numerical tests which confirm the effectiveness of the theoretical results and the performance of the proposed neural network.
KeywordsSteepest descent neural network Differential inclusion-based methods General nonsmooth convex optimization Convergence of trajectories
The authors would like to thank the editor and the reviewers of the paper for their instructive comments. Certainly, their meticulous reading and fruitful comments enriched the content and the structure of this paper.
- 1.Mordukhovich, B.: Variations Analysis and Generalized Differentiation, I: Basic Theory. Springer, Berlin (2006) Google Scholar
- 2.Mordukhovich, B.: Variations Analysis and Generalized Differentiation, II: Applications. Springer, Berlin (2006) Google Scholar
- 7.Hiriart-Urruty, J.B., Lemaréchal, C.: Convex Analysis and Minimization Algorithms: Part 2: Advanced Theory and Bundle Methods. Springer, Berlin (2010) Google Scholar
- 31.Lukšan, L., Vlček, J.: Test problems for nonsmooth unconstrained and linearly constrained optimization. Institute of Computer Science, Academy of Science of the Czech Republic, Technical report, 798 (2000) Google Scholar