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Characterizing Nonemptiness and Compactness of the Solution Set of a Convex Vector Optimization Problem with Cone Constraints and Applications.
- Source :
-
Journal of Optimization Theory & Applications . Nov2004, Vol. 123 Issue 2, p391-407. 17p. - Publication Year :
- 2004
-
Abstract
- In this paper, we characterize the nonemptiness and compactness of the set of weakly efficient solutions of a convex vector optimization problem with cone constraints in terms of the level-boundedness of the component functions of the objective on the perturbed sets of the original constraint set. This characterization is then applied to carry out the asymptotic analysis of a class of penalization methods. More specifically, under the assumption of nonemptiness and compactness of the weakly efficient solution set, we prove the existence of a path of weakly efficient solutions to the penalty problem and its convergence to a weakly efficient solution of the original problem. Furthermore, for any efficient point of the original problem, there exists a path of efficient solutions to the penalty problem whose function values (with respect to the objective function of the original problem) converge to this efficient point. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00223239
- Volume :
- 123
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Optimization Theory & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 15388705
- Full Text :
- https://doi.org/10.1007/s10957-004-5155-z