Solving minimax problems : Local smoothing versus global smoothing
- Authors: Bagirov, Adil , Sultanova, Nargiz , Al Nuaimat, Alia , Taheri, Sona
- Date: 2018
- Type: Text , Conference proceedings
- Relation: 4th International Conference on Numerical Analysis and Optimization, NAO-IV 2017; Muscat, Oman; 2nd-5th January 2017; published in Numerical Analysis and Optimization NAO-IV (part of the Springer Proceedings in Mathematics and Statistics book series PROMS, volume 235) Vol. 235, p. 23-43
- Full Text: false
- Reviewed:
- Description: The aim of this chapter is to compare different smoothing techniques for solving finite minimax problems. We consider the local smoothing technique which approximates the function in some neighborhood of a point of nondifferentiability and also global smoothing techniques such as the exponential and hyperbolic smoothing which approximate the function in the whole domain. Computational results on the collection of academic test problems are used to compare different smoothing techniques. Results show the superiority of the local smoothing technique for convex problems and global smoothing techniques for nonconvex problems. © 2018, Springer International Publishing AG, part of Springer Nature.
- Description: Springer Proceedings in Mathematics and Statistics
An incremental clustering algorithm based on hyperbolic smoothing
- Authors: Bagirov, Adil , Ordin, Burak , Ozturk, Gurkan , Xavier, Adilson
- Date: 2015
- Type: Text , Journal article
- Relation: Computational Optimization and Applications Vol. 61, no. 1 (2015), p. 219-241
- Relation: http://purl.org/au-research/grants/arc/DP140103213
- Full Text: false
- Reviewed:
- Description: Clustering is an important problem in data mining. It can be formulated as a nonsmooth, nonconvex optimization problem. For the most global optimization techniques this problem is challenging even in medium size data sets. In this paper, we propose an approach that allows one to apply local methods of smooth optimization to solve the clustering problems. We apply an incremental approach to generate starting points for cluster centers which enables us to deal with nonconvexity of the problem. The hyperbolic smoothing technique is applied to handle nonsmoothness of the clustering problems and to make it possible application of smooth optimization algorithms to solve them. Results of numerical experiments with eleven real-world data sets and the comparison with state-of-the-art incremental clustering algorithms demonstrate that the smooth optimization algorithms in combination with the incremental approach are powerful alternative to existing clustering algorithms.