Characterizing Nonemptiness and Compactness of the Solution Set of a Convex Vector Optimization Problem with Cone Constraints and Applications

X. X. Huang, X. Q. Yang and K. L. Teo
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X. X. Huang: Chongqing Normal University
X. Q. Yang: Hong Kong Polytechnic University
K. L. Teo: Hong Kong Polytechnic University

Journal of Optimization Theory and Applications, 2004, vol. 123, issue 2, No 9, 407 pages

Abstract: 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.

Keywords: Optimization problem with cone constraints; weakly efficient solutions; efficient solutions; penalization methods (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s10957-004-5155-z

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