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.
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Communicated by Masao Fukushima and Liqun Qi
This work is supported by the Postdoctoral Fellowship of Hong Kong Polytechnic University.
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X. Huang, X., Teo, K.L. & Yang, X.Q. Calmness and Exact Penalization in Vector Optimization with Cone Constraints. Comput Optim Applic 35, 47–67 (2006). https://doi.org/10.1007/s10589-006-6441-5
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DOI: https://doi.org/10.1007/s10589-006-6441-5