First Order Characterizations of Pseudoconvex Functions
In this paper the author proposes a generalization of the notion of pseudoconvexity given by Mangasarian for differentiable functions by replacing the (directional) derivative by an appropriate abstract function. Under certain conditions on this abstract ``derivative'', characterizations of this notion of pseudoconvexity are obtained. As a natural consequence first order optimality conditions for such functions are proved. Another application is a criterion for a quasiconvex function to be pseudoconvex. Finally, monotone type properties of the abstract derivatives are studied.
- Bulgarian Academy of Sciences Bulgaria
- Institute of Mathematics and Informatics Bulgaria
generalized convexity, Nonsmooth Function, Pseudomonotone Generalized Directional Derivative, Convex programming, Invex Function, Nonsmooth analysis, quasiconvex function, Quasiconvex Function, pseudoconvex function, Nonsmooth Optimization, Solution Sets, Generalized Directional Derivative, Pseudoconvex Function, directional derivative, Generalized Convexity, Convexity of real functions of several variables, generalizations
generalized convexity, Nonsmooth Function, Pseudomonotone Generalized Directional Derivative, Convex programming, Invex Function, Nonsmooth analysis, quasiconvex function, Quasiconvex Function, pseudoconvex function, Nonsmooth Optimization, Solution Sets, Generalized Directional Derivative, Pseudoconvex Function, directional derivative, Generalized Convexity, Convexity of real functions of several variables, generalizations
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