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

Authors:
Ning Ruan;David Yang Gao
Affiliations:
School of Sciences, Information Technology and Engineering, University of Ballarat, Ballarat, VIC, Australia,Department of Mathematics and Statistics, Curtin University, Perth, WA, Australia;School of Sciences, Information Technology and Engineering, University of Ballarat, Ballarat, VIC, Australia
Venue:
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part III
Year:
2012

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Abstract

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.