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On locally Lipschitz vector-valued invex functions. (English) Zbl 0786.90054
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 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.
MSC:
90C26Nonconvex programming, global optimization
49J52Nonsmooth analysis (other weak concepts of optimality)