Necessary Optimality Conditions in Terms of Convexificators in Lipschitz Optimization

X. F. Li and J. Z. Zhang
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X. F. Li: Jilin University
J. Z. Zhang: City University of Hong Kong

Journal of Optimization Theory and Applications, 2006, vol. 131, issue 3, No 8, 429-452

Abstract: Abstract This study is devoted to constraint qualifications and Kuhn-Tucker type necessary optimality conditions for nonsmooth optimization problems involving locally Lipschitz functions. The main tool of the study is the concept of convexificators. First, the case of a minimization problem in the presence of an arbitrary set constraint is considered by using the contingent cone and the adjacent cone to the constraint set. Then, in the case of a minimization problem with inequality constraints, Abadie type constraint qualifications and several other qualifications are proposed; Kuhn-Tucker type necessary optimality conditions are derived under the qualifications.

Keywords: Locally Lipschitz functions; Dini derivatives; convexificators; constraint qualifications; necessary optimality conditions; nonsmooth optimizations (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-006-9155-z

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