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Quasiconvex, pseudoconvex, and strictly pseudoconvex quadratic functions

Name: Quasiconvex, pseudoconvex, and strictly pseudoconvex quadratic functions
Creator: Siegfried Schaible
Keywords: Convex programming, strictly pseudoconvex quadratic functions, pseudoconvex functions, 0211 other engineering and technologies, 02 engineering and technology, 0101 mathematics, quasi-convex functions, 01 natural sciences, Convexity of real functions in one variable, generalizations

descriptionPublicationkeyboard_double_arrow_right Article 01 Nov 1981Publisher:Springer Science and Business Media LLCJournal:Journal of Optimization Theory and Applications, volume 35, pages 303-338 (issn: 0022-3239, eissn: 1573-2878,

Authors: Siegfried Schaible;

doi: 10.1007/bf00934906

Quasiconvex, pseudoconvex, and strictly pseudoconvex quadratic functions

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Abstract

The purpose of this paper is twofold. Firstly, criteria for quasiconvex and pseudoconvex quadratic functions in nonnegative variables of Cottle, Ferland, and Martos are derived by specializing criteria proved by the author. We do not make use of the concept of positive subdefinite matrices. Instead, we are specializing criteria that were derived for quadratic functions on arbitrary convex sets to the special case of quadratic functions in nonnegative variables. The second purpose of this paper is to present several new criteria involving also strictly pseudoconvex quadratic functions.

Related Organizations

University of Alberta
Canada

Keywords

Convex programming, strictly pseudoconvex quadratic functions, pseudoconvex functions, quasi-convex functions, Convexity of real functions in one variable, generalizations

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