Global solutions to fractional programming problem with ratio of nonconvex functions
- Authors: Ruan, Ning , Gao, David
- Date: 2015
- Type: Text , Journal article
- Relation: Applied Mathematics and Computation Vol. 255, no. (2015), p. 66-72
- Full Text: false
- Reviewed:
- Description: This paper presents a canonical dual approach for minimizing a sum of quadratic function and a ratio of nonconvex functions in Rn. By introducing a parameter, the problem is first equivalently reformed as a nonconvex polynomial minimization with elliptic constraint. It is proved that under certain conditions, the canonical dual is a concave maximization problem in R2 that exhibits no duality gap. Therefore, the global optimal solution of the primal problem can be obtained by solving the canonical dual problem. © 2014 Elsevier Inc. All rights reserved.
An efficient classification using support vector machines
- Authors: Ruan, Ning , Chen, Yi , Gao, David
- Date: 2013
- Type: Text , Conference paper
- Relation: Proceedings of 2013 Science and Information Conference, SAI 2013 p. 585-589
- Full Text: false
- Reviewed:
- Description: Support vector machine (SVM) is a popular method for classification in data mining. The canonical duality theory provides a unified analytic solution to a wide range of discrete and continuous problems in global optimization. This paper presents a canonical duality approach for solving support vector machine problem. It is shown that by the canonical duality, these nonconvex and integer optimization problems are equivalent to a unified concave maximization problem over a convex set and hence can be solved efficiently by existing optimization techniques. © 2013 The Science and Information Organization.
Canonical dual approach for minimizing a nonconvex quadratic function over a sphere
- Authors: Chen, Yi , Gao, David
- Date: 2013
- Type: Text , Conference paper
- Relation: 3rd World Congress on Global Optimization in Engineering and Science, WCGO 2013; Anhui, China; 8th-12th July 2013 Vol. 95, p. 149-156
- Full Text: false
- Reviewed:
- Description: In this paper, we study global optimal solutions of minimizing a nonconvex quadratic function subject to a sphere constraint. The main challenge is to solve the problem when it has multiple global solutions on the boundary of the sphere, which is called hard case. By canonical duality theory, a concave maximization problem is formulated, which is one-dimensional and without duality gaps to the primal problem. Then sufficient and necessary conditions are provided to identify whether the problem is in the hard case or not. A perturbation method and associated algorithms are proposed to solve hard-case problems. Theoretical results and methods are verified by numerical examples. © Springer International Publishing Switzerland 2015.
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
- Full Text:
- Reviewed:
- 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