On second order conditions for quasiconvexity

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1980 English Publisher:Springer Science and Business Media LLCJournal:Mathematical Programming, volume 18, pages 349-352 (issn: 0025-5610, eissn: 1436-4646,

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Authors: Jean-Pierre Crouzeix;

doi: 10.1007/bf01588330

On second order conditions for quasiconvexity

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Abstract

The paper presents a sufficient condition for quasiconvexity in terms of Hessian, hereby extending an earlier result by Katzner in 1970, and (by a slight modification of the assumptions) a necessary and sufficient condition for quasiconvexity.

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Keywords

Convex programming, quasiconvexity, second order conditions, twice differentiable functions, pseudoconvexity, Convexity of real functions of several variables, generalizations, necessary and sufficient condition

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