Calmness and Exact Penalization in Vector Optimization with Cone Constraints

Authors:
X. X. Huang;K. L. Teo;X. Q. Yang
Affiliations:
Aff1 Aff2;Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong;Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong
Venue:
Computational Optimization and Applications
Year:
2006

Citing 7
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Abstract

In this paper, a (local) calmness condition of order 驴 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 驴 are established. Finally, it is shown that the local calmness of order 1 implies the existence of normal Lagrange multipliers.