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Zbl 0786.90054
Yen, N.D.; Sach, P.H.
On locally Lipschitz vector-valued invex functions. (English)
[J] Bull. Aust. Math. Soc. 47, No.2, 259-272 (1993). ISSN 0004-9727

Summary: The four types of invexity for locally Lipschitz vector-valued functions recently introduced by T. W. Reiland are studied in more detail. It is shown that the class of restricted $K$-invex in the limit functions is too large to obtain desired optimization theorems and the other three classes are contained in the class of functions which are invex 0 in the sense of our previous joint paper with {\it B. D. Craven} and {\it T. D. Phuong} [`A new class of invex multifunctions', to appear]. We also prove that the extended image of a locally Lipschitz vector-valued invex function is pseudoconvex in the sense of {\it J. Borwein} [SIAM J. Control Optimization 16, 512-522 (1978; Zbl 0383.90109)] at each of its points.

MSC 2000:: *90C26 Nonconvex programming
49J52 Nonsmooth analysis (other weak concepts of optimality)

Keywords: locally Lipschitz vector-valued functions

Citations: Zbl 0383.90109

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