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Authors: Karmitsa, Napsu , Bagirov, Adil , Makela, Marko
Date: 2012
Type: Text , Journal article
Relation: Optimization Methods and Software Vol. 27, no. 1 (2012), p. 131-153
Relation: http://purl.org/au-research/grants/arc/DP0666061
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Description: Most nonsmooth optimization (NSO) methods can be divided into two main groups: subgradient methods and bundle methods. In this paper, we test and compare different methods from both groups as well as some methods which may be considered as hybrids of these two and/or some others. All the solvers tested are so-called general black box methods which, at least in theory, can be applied to solve almost all NSO problems. The test set includes a large number of unconstrained nonsmooth convex and nonconvex problems of different size. In particular, it includes piecewise linear and quadratic problems. The aim of this work is not to foreground some methods over the others but to get some insight on which method to select for certain types of problems. © 2012 Taylor and Francis Group, LLC.

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Canonical duality theory and algorithm for solving challenging problems in network optimisation

Authors: Ruan, Ning , Gao, David
Date: 2012
Type: Text , Conference paper
Relation: 19th International Conference on Neural Information Processing, ICONIP 2012 Vol. 7665 LNCS, p. 702-709
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Description: This paper presents a canonical dual approach for solving a general nonconvex problem in network optimization. Three challenging problems, sensor network location, traveling salesman problem, and scheduling problem are listed to illustrate the applications of the proposed method. It is shown that by the canonical duality, these nonconvex and integer optimization problems are equivalent to unified concave maximization problem over a convex set and hence can be solved efficiently by existing optimization techniques. © 2012 Springer-Verlag.
Description: 2003010653

Authors: Latorre, Vittorio , Gao, David
Date: 2013
Type: Text , Journal article
Relation: Advances in Intelligent Systems and Computing Vol. 212, no. (2013), p. 1189-1197
Full Text: false
Reviewed:
Description: Radial Basis Function Neural Networks (RBF NN) are a tool largely used for regression problems. The principal drawback of this kind of predictive tool is that the optimization problem solved to train the network can be non-convex. On the other hand Canonical Duality Theory offers a powerful procedure to reformulate general non-convex problems in dual forms so that it is possible to find optimal solutions and to get deep insights into the nature of the challenging problems. By combining the canonical duality theory with the RBF NN, this paper presents a potentially useful method for solving challenging problems in real-world applications. © Springer-Verlag Berlin Heidelberg 2013. Proceedings of the Eighth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA), 2013.
Description: 2003011221

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