Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/14950
Title: Characterizing nonemptiness and compactness of the solution set of a convex vector optimization problem with cone constraints and applications
Authors: Huang, XX
Yang, XQ 
Teo, KL
Keywords: Efficient solutions
Optimization problem with cone constraints
Penalization methods
Weakly efficient solutions
Issue Date: 2004
Publisher: Springer
Source: Journal of optimization theory and applications, 2004, v. 123, no. 2, p. 391-407 How to cite?
Journal: Journal of optimization theory and applications 
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.
URI: http://hdl.handle.net/10397/14950
ISSN: 0022-3239
EISSN: 1573-2878
DOI: 10.1007/s10957-004-5155-z
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