Canonical dual approach to solving the maximum cut problem
- Authors: Wang, Zhenbo , Fang, Shucherng , Gao, David , Xing, Wenxun
- Date: 2012
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. , no. (2012), p. 1-11
- Full Text: false
- Reviewed:
- Description: This paper presents a canonical dual approach for finding either an optimal or approximate solution to the maximum cut problem (MAX CUT). We show that, by introducing a linear perturbation term to the objective function, the maximum cut problem is perturbed to have a dual problem which is a concave maximization problem over a convex feasible domain under certain conditions. Consequently, some global optimality conditions are derived for finding an optimal or approximate solution. A gradient decent algorithm is proposed for this purpose and computational examples are provided to illustrate the proposed approach. © 2012 Springer Science+Business Media, LLC.
Global optimal solutions to a class of quadrinomial minimization problems with one quadratic constraint
- Authors: Yuan, Y. B. , Fang, Shucherng , Gao, David
- Date: 2012
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 52, no. 2 (2012), p. 195-209
- Full Text: false
- Reviewed:
- Description: This paper studies the canonical duality theory for solving a class of quadri- nomial minimization problems subject to one general quadratic constraint. It is shown that the nonconvex primal problem in Rn can be converted into a concave maximization dual problem over a convex set in R2 , such that the problem can be solved more efficiently. The existence and uniqueness theorems of global minimizers are provided using the triality theory. Examples are given to illustrate the results obtained. © 2011 Springer Science+Business Media, LLC.