Constraint Qualifications in Nonsmooth Multiobjective Optimization

X. F. Li
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X. F. Li: Jilin University of Technology

Journal of Optimization Theory and Applications, 2000, vol. 106, issue 2, No 7, 373-398

Abstract: Abstract For an inequality constrained nonsmooth multiobjective optimization problem involving locally Lipschitz functions, stronger KT-type necessary conditions and KT necessary conditions (which in the continuously differentiable case reduce respectively to the stronger KT conditions studied recently by Maeda and the usual KT conditions) are derived for efficiency and weak efficiency under several constraint qualifications. Stimulated by the stronger KT-type conditions, the notion of core of the convex hull of the union of finitely many convex sets is introduced. As main tool in the derivation of the necessary conditions, a theorem of the alternatives and a core separation theorem are also developed which are respectively extensions of the Motzkin transposition theorem and the Tucker theorem.

Keywords: nonsmooth multiobjective optimization; constraint qualifications; KT necessary conditions; Lipschitz continuity; Clarke subdifferential (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (10)

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DOI: 10.1023/A:1004607615343

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