Subgradient Method for Nonconvex Nonsmooth Optimization

In this paper, we introduce a new method for solving nonconvex nonsmooth optimization problems. It uses quasisecants, which are subgradients computed in some neighborhood of a point. The proposed method contains simple procedures for finding descent directions and for solving line search subproblems...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2013-05, Vol.157 (2), p.416-435
Main Authors: Bagirov, A. M., Jin, L., Karmitsa, N., Al Nuaimat, A., Sultanova, N.
Format: Article
Language:English
Subjects:
Algorithms
Applications of Mathematics
Bundling
Calculus of Variations and Optimal Control
Optimization
Computation
Convergence
Convex analysis
Descent
Engineering
Experiments
Mathematical models
Mathematics
Mathematics and Statistics
Methods
Neighborhoods
Operations Research/Decision Theory
Optimization
Problem solving
Searching
Studies
Theory of Computation
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Summary:In this paper, we introduce a new method for solving nonconvex nonsmooth optimization problems. It uses quasisecants, which are subgradients computed in some neighborhood of a point. The proposed method contains simple procedures for finding descent directions and for solving line search subproblems. The convergence of the method is studied and preliminary results of numerical experiments are presented. The comparison of the proposed method with the subgradient and the proximal bundle methods is demonstrated using results of numerical experiments.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-012-0167-6