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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
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