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On locally Lipschitz vector-valued invex functions

Published online by Cambridge University Press:  17 April 2009

N.D. Yen  and
P.H. Sach
N.D. Yen
Affiliation:
Institute of Mathematics, PO Box 631, Bo Ho 10000 Hanoi, Vietnam
P.H. Sach
Affiliation:
Institute of Mathematics, PO Box 631, Bo Ho 10000 Hanoi, Vietnam
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Abstract

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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 optimisation 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 B. D. Craven and T. D. Phuong. We also prove that the extended image of a locally Lipschitz vector-valued invex function is pseudoconvex in the sense of J. Borwein at each of its points.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 47 , Issue 2 , April 1993 , pp. 259 - 272
Copyright
Copyright © Australian Mathematical Society 1993

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