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Semistrictly preinvex functions. (English) Zbl 0985.26007

A class of functions, called semistrictly preinvex functions is defined. This is a generalization of the class of preinvex functions introduced by T. Weir and B. Mond [J. Math. Anal. Appl. 136, No. 1, 29-38 (1988; Zbl 0663.90087)] and by T. Weir and V. Jeyakumar [Bull. Aust. Math. Soc. 38, No. 2, 177-189 (1988; Zbl 0639.90082)]. It is shown that for the functions of this new class any local minimizer is global. A relationship between preinvex functions and semistrictly preinvex functions and some properties of semistrictly preinvex functions are also given.

MSC:

26B25 Convexity of real functions of several variables, generalizations
90C29 Multi-objective and goal programming
90C30 Nonlinear programming
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