Lipschitz B-Vex Functions and Nonsmooth Programming

X. F. Li, J. L. Dong and Q. H. Liu
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X. F. Li: Jilin University of Technology
J. L. Dong: Jilin University of Technology
Q. H. Liu: Jilin University of Technology

Journal of Optimization Theory and Applications, 1997, vol. 93, issue 3, No 7, 557-574

Abstract: Abstract In this paper, the equivalence between the class of B-vex functions and that of quasiconvex functions is proved. Necessary and sufficient conditions, under which a locally Lipschitz function is B-vex, are established in terms of the Clarke subdifferential. Regularity of locally Lipschitz B-vex functions is discussed. Furthermore, under appropriate conditions, a necessary optimality condition of the Slater type and a sufficient optimality condition are obtained for a nonsmooth programming problem involving B-vex functions.

Keywords: B-vex functions; quasiconvex functions; subdifferentials; regularity; optimality conditions (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (2)

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DOI: 10.1023/A:1022643129733

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