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On $$(E,F)$$ generalized convexity. (English) Zbl 1165.90643
Summary: A class of $$(E,F)$$ generalized convexity is introduced, which includes $$(E,F)$$-convex sets, $$(E,F)$$-convex functions and $$(E,F)$$-convex programming. This kind of generalized convexity is based on a pair of point-to-set map $$(E,F)$$ and the properties of the given sets and the given functions. Some important properties of these three new notions are established. Finally, some results in [E. A. Youness, J. Optimization Theory Appl. 102, No. 2, 439–450 (1999; Zbl 0937.90082)] for E-convex functions and E-convex programming are pointed to be incorrect.

##### MSC:
 90C30 Nonlinear programming 65K05 Numerical mathematical programming methods