Subgradient Method for Nonconvex Nonsmooth Optimization

- Bagirov, Adil, Jin, L., Karmitsa, Napsu, Al Nuaimat, A., Sultanova, Nargiz

  • 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
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  • 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.

Nonsmooth optimization algorithm for solving clusterwise linear regression problems

- Bagirov, Adil, Ugon, Julien, Mirzayeva, Hijran

  • Authors: Bagirov, Adil , Ugon, Julien , Mirzayeva, Hijran
  • Date: 2015
  • Type: Text , Journal article
  • Relation: Journal of Optimization Theory and Applications Vol. 164, no. 3 (2015), p. 755-780
  • Relation: http://purl.org/au-research/grants/arc/DP140103213
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  • Description: Clusterwise linear regression consists of finding a number of linear regression functions each approximating a subset of the data. In this paper, the clusterwise linear regression problem is formulated as a nonsmooth nonconvex optimization problem and an algorithm based on an incremental approach and on the discrete gradient method of nonsmooth optimization is designed to solve it. This algorithm incrementally divides the whole dataset into groups which can be easily approximated by one linear regression function. A special procedure is introduced to generate good starting points for solving global optimization problems at each iteration of the incremental algorithm. The algorithm is compared with the multi-start Spath and the incremental algorithms on several publicly available datasets for regression analysis.

Aggregate codifferential method for nonsmooth DC optimization

- Tor, Ali, Bagirov, Adil, Karasozen, Bulent

  • Authors: Tor, Ali , Bagirov, Adil , Karasozen, Bulent
  • Date: 2014
  • Type: Text , Journal article
  • Relation: Journal of Computational and Applied Mathematics Vol. 259, no. Part B (2014), p. 851-867
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  • Description: A new algorithm is developed based on the concept of codifferential for minimizing the difference of convex nonsmooth functions. Since the computation of the whole codifferential is not always possible, we use a fixed number of elements from the codifferential to compute the search directions. The convergence of the proposed algorithm is proved. The efficiency of the algorithm is demonstrated by comparing it with the subgradient, the truncated codifferential and the proximal bundle methods using nonsmooth optimization test problems.
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