Univex sets, functions and univex nonlinear programming. (English) Zbl 0802.90092

Komlósi, Sándor (ed.) et al., Proceedings of the 5th international workshop on generalized convexity held at Janus Pannonius University, Pécs, Hungary, August 31-September 2, 1992. Berlin: Springer-Verlag. Lect. Notes Econ. Math. Syst. 405, 3-18 (1994).
Summary: We introduce the concept of univex sets, and define a new class of functions, called univex functions, on them. These functions unify the concepts of convexity, \(B\)-vexity, invexity and \(B\)-invexity. Some of their properties are proved and applications in nonlinear programming are discussed. Furthermore, generalized univex functions are also introduced and their relationships to univex functions and convex (generalized convex) functions are also discussed. Under appropriate assumptions of univexity, optimality conditions and duality results for Mond-Weir duality are established. In the end some suggestions for further research have been made.
For the entire collection see [Zbl 0788.00061].


90C30 Nonlinear programming
26B25 Convexity of real functions of several variables, generalizations