Higher-order Pseudoconvex Functions

Ivan Ginchev () and Vsevolod I. Ivanov ()
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Ivan Ginchev: Technical University of Varna
Vsevolod I. Ivanov: Technical University of Varna

A chapter in Generalized Convexity and Related Topics, 2007, pp 247-264 from Springer

Abstract: Summary In terms of n-th order Dini directional derivative with n positive integer we define n-pseudoconvex functions being a generalization of the usual pseudoconvex functions. Again with the n-th order Dini derivative we define n-stationary points, and prove that a point x 0 is a global minimizer of a n-pseudoconvex function f if and only if x 0 is a n-stationary point of f. Our main result is the following. A radially continuous function f defined on a radially open convex set in a real linear space is n-pseudoconvex if and only if f is quasiconvex function and any n-stationary point is a global minimizer. This statement generalizes the results of Crouzeix, Ferland, Math. Program. 23 (1982), 193–205, and Komlósi, Math. Program. 26 (1983), 232–237. We study also other aspects of the n-pseudoconvex functions, for instance their relations to variational inequalities.

Keywords: Pseudoconvex functions; n-pseudoconvex functions; stationary points; n-stationary points; quasiconvex functions (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/978-3-540-37007-9_14

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