A class of convexification and concavification methods for non-monotone optimization problems
- Authors: Wu, Zhiyou , Lee, Heung , Yang, Xin-Min
- Date: 2005
- Type: Text , Journal article
- Relation: Optimization Vol. 54, no. 6 (2005), p. 605-625
- Full Text: false
- Reviewed:
- Description: A class of convexification and concavification methods are proposed for solving some classes of non-monotone optimization problems. It is shown that some classes of non-monotone optimization problems can be converted into better structured optimization problems, such as, concave minimization problems, reverse convex programming problems, and canonical D.C. programming problems by the proposed convexification and concavification methods. The equivalence between the original problem and the converted better structured optimization problem is established.
- Description: C1
- Description: 2003003608
Peeling off a nonconvex cover of an actual convex problem: Hidden convexity
- Authors: Wu, Zhiyou , Li, Duan , Zhang, Lian-Sheng , Yang, Xin-Min
- Date: 2007
- Type: Text , Journal article
- Relation: SIAM Journal on Optimization Vol. 18, no. 2 (2007), p. 507-536
- Full Text: false
- Reviewed:
- Description: Convexity is, without a doubt, one of the most desirable features in optimization. Many optimization problems that are nonconvex in their original settings may become convex after performing certain equivalent transformations. This paper studies the conditions for such hidden convexity. More specifically, some transformation-independent sufficient conditions have been derived for identifying hidden convexity. The derived sufficient conditions are readily verifiable for quadratic optimization problems. The global minimizer of a hidden convex programming problem can be identified using a local search algorithm. © 2007 Society for Industrial and Applied Mathematics.
- Description: C1
- Description: 2003005616