Results

**1 - 1**of**1**### CONSTRUCTION OF VALIDATED UNIQUENESS REGIONS FOR NONLINEAR PROGRAMS IN WHICH CONVEX SUBSPACES HAVE BEEN Identified

, 2005

"... In deterministic global optimization algorithms for constrained problems, it can be advantageous to identify and utilize coordinates in which the problem is convex, as Epperly and Pistikopoulos have done. In self-validating versions of these algorithms, a useful technique is to construct regions a ..."

Abstract
- Add to MetaCart

(Show Context)
In deterministic global optimization algorithms for constrained problems, it can be advantageous to identify and utilize coordinates in which the problem is convex, as Epperly and Pistikopoulos have done. In self-validating versions of these algorithms, a useful technique is to construct regions about approximate optima, within which unique local optima are known to exist; these regions are to be as large as possible, for exclusion from the continuing search process. In this paper, we clarify the theory and develop algorithms for constructing such large regions, when we know the problem is convex in some of the variables. In addition, this paper clarifies how one can validate existence and uniqueness of local minima when using the Fritz John equations in the general case. We present numerical results that provide evidence of the efficacy of our techniques.