Programming with semilocally quasiconvex functions (Q1079128)

The concept of semilocally quasiconvex and semilocally pseudoconvex functions was introduced in a previous paper of the author and \textit{S. Kaur} [Eur. J. Oper. Res. 9, 369-377 (1982; Zbl 0501.90090)] as a generalization of quasiconvex and pseudoconvex functions. This paper presents a sufficient condition of Kuhn-Tucker type for a minimization problem in which the objective function and the feasible set are given by semilocally quasiconvex functions. A first order sufficient condition for semilocal pseudoconvexity of a semilocally quasiconvex function is also given.