A proximal bundle method for nonsmooth DC optimization utilizing nonconvex cutting planes
- Authors: Joki, Kaisa , Bagirov, Adil , Karmitsa, Napsu , Makela, Marko
- Date: 2017
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 68, no. 3 (2017), p. 501-535
- Relation: http://purl.org/au-research/grants/arc/DP140103213
- Full Text: false
- Reviewed:
- Description: In this paper, we develop a version of the bundle method to solve unconstrained difference of convex (DC) programming problems. It is assumed that a DC representation of the objective function is available. Our main idea is to utilize subgradients of both the first and second components in the DC representation. This subgradient information is gathered from some neighborhood of the current iteration point and it is used to build separately an approximation for each component in the DC representation. By combining these approximations we obtain a new nonconvex cutting plane model of the original objective function, which takes into account explicitly both the convex and the concave behavior of the objective function. We design the proximal bundle method for DC programming based on this new approach and prove the convergence of the method to an -critical point. The algorithm is tested using some academic test problems and the preliminary numerical results have shown the good performance of the new bundle method. An interesting fact is that the new algorithm finds nearly always the global solution in our test problems.
Limited memory discrete gradient bundle method for nonsmooth derivative-free optimization
- Authors: Karmitsa, Napsu , Bagirov, Adil
- Date: 2012
- Type: Text , Journal article
- Relation: Optimization Vol. 61, no. 12 (2012), p. 1491-1509
- Full Text: false
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- Description: Typically, practical nonsmooth optimization problems involve functions with hundreds of variables. Moreover, there are many practical problems where the computation of even one subgradient is either a difficult or an impossible task. In such cases derivative-free methods are the better (or only) choice since they do not use explicit computation of subgradients. However, these methods require a large number of function evaluations even for moderately large problems. In this article, we propose an efficient derivative-free limited memory discrete gradient bundle method for nonsmooth, possibly nonconvex optimization. The convergence of the proposed method is proved for locally Lipschitz continuous functions and the numerical experiments to be presented confirm the usability of the method especially for medium size and large-scale problems. © 2012 Copyright Taylor and Francis Group, LLC.
- Description: 2003010398
Subgradient Method for Nonconvex Nonsmooth Optimization
- Authors: Bagirov, Adil , Jin, L. , Karmitsa, Napsu , Al Nuaimat, A. , Sultanova, Nargiz
- Date: 2012
- Type: Text , Journal article
- Relation: Journal of Optimization Theory and Applications Vol.157, no.2 (2012), p.416–435
- Full Text: false
- Reviewed:
- Description: 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. © 2012 Springer Science+Business Media, LLC.