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Optimality and duality with generalized convexity. (English) Zbl 0838.90114

Summary: Hanson and Mond have given sets of necessary and sufficient conditions for optimality and duality in constrained optimization by introducing classes of generalized convex functions, called type I and type II functions. Recently, Bector defined univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, optimality and duality results for several mathematical programs are obtained combining the concepts of type I and univex functions. Examples of functions satisfying these conditions are given.

MSC:

90C30 Nonlinear programming
26B25 Convexity of real functions of several variables, generalizations
90C32 Fractional programming
90C29 Multi-objective and goal programming
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