Calmness and Exact Penalization in Vector Optimization with Cone Constraints |
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Authors: | X. X. Huang K. L. Teo X. Q. Yang |
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Affiliation: | (1) Department of Mathematics and Computer Science, Chongqing Normal University, Chongqing, 400047, China;(2) Present address: Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong |
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Abstract: | In this paper, a (local) calmness condition of order α is introduced for a general vector optimization problem with cone constraints in infinite dimensional spaces. It is shown that the (local) calmness is equivalent to the (local) exact penalization of a vector-valued penalty function for the constrained vector optimization problem. Several necessary and sufficient conditions for the local calmness of order α are established. Finally, it is shown that the local calmness of order 1 implies the existence of normal Lagrange multipliers. Presented at the 6th International Conference on Optimization: Techniques and Applications, Ballarat, Australia, December 9–11, 2004 This work is supported by the Postdoctoral Fellowship of Hong Kong Polytechnic University. |
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Keywords: | vector optimization with cone constraints weakly efficient solution efficient solution calmness exact penalization normal Lagrange multiplier |
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