Properties of strongly star shaped cones
- Authors: Morales-Silva, Daniel
- Date: 2007
- Type: Text , Journal article
- Relation: Pacific Journal of Optimization Vol. 3, no. 2 (2007), p. 379-386
- Full Text: false
- Reviewed:
- Description: In problems of vector optimization, with preferences that are not necessarily a pre-order relation, the strongly star shaped cones are very important in order to get a scalarization of these problems. In this work we present some properties of these cones and also a characterization for a special type.
- Description: C1
- Description: 2003004940
Complete solutions and triality theory to a nonconvex optimization problem with double-well potential in Rn
- Authors: Morales-Silva, Daniel , Gao, David
- Date: 2013
- Type: Text , Journal article
- Relation: Numerical Algebra, Control and Optimization Vol. 3, no. 2 (2013), p. 271-282
- Full Text:
- Reviewed:
- Description: The main purpose of this research note is to show that the triality theory can always be used to identify both global minimizer and the biggest local maximizer in global optimization. An open problem left on the double- min duality is solved for a nonconvex optimization problem with double-well potential in ℝn, which leads to a complete set of analytical solutions. Also a convergency theorem is proved for linear perturbation canonical dual method, which can be used for solving global optimization problems with multiple so- lutions. The methods and results presented in this note pave the way towards the proof of the triality theory in general cases.