Bulletin of the Australian Mathematical Society

Research Article

On locally Lipschitz vector-valued invex functions

N.D. Yena1 and P.H. Sacha1

a1 Institute of Mathematics, PO Box 631, Bo Ho 10000 Hanoi, Vietnam


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.

(Received March 16 1992)