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
-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 B. D. Craven
and 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 J. Borwein
[SIAM J. Control Optimization 16, 512-522 (1978; Zbl 0383.90109
)] at each of its points.