There are many totally convex functions

Dan Butnariu; Simeon Reich; Alexander J. Zaslavski

There are many totally convex functions

Dan Butnariu, Simeon Reich, Alexander J. Zaslavski

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let K be a convex subset of a normed linear space and let R¹ denote the real line. We show that there are many (in the sense of Bake category) strictly convex and totally convex functions f : K → R ¹. It is known that the existence of such functions is crucial in numerous optimization algorithms.

Original language	English
Pages (from-to)	623-632
Number of pages	10
Journal	Journal of Convex Analysis
Volume	13
Issue number	3-4
State	Published - 2006

Keywords

Complete metric space
Essentially strictly convex function
Generic property
Strictly convex function
Totally convex function

ASJC Scopus subject areas

Analysis
General Mathematics

Cite this

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title = "There are many totally convex functions",

abstract = "Let K be a convex subset of a normed linear space and let R1 denote the real line. We show that there are many (in the sense of Bake category) strictly convex and totally convex functions f : K → R 1. It is known that the existence of such functions is crucial in numerous optimization algorithms.",

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AU - Butnariu, Dan

AU - Reich, Simeon

AU - Zaslavski, Alexander J.

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N2 - Let K be a convex subset of a normed linear space and let R1 denote the real line. We show that there are many (in the sense of Bake category) strictly convex and totally convex functions f : K → R 1. It is known that the existence of such functions is crucial in numerous optimization algorithms.

AB - Let K be a convex subset of a normed linear space and let R1 denote the real line. We show that there are many (in the sense of Bake category) strictly convex and totally convex functions f : K → R 1. It is known that the existence of such functions is crucial in numerous optimization algorithms.

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KW - Essentially strictly convex function

KW - Generic property

KW - Strictly convex function

KW - Totally convex function

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M3 - Article

AN - SCOPUS:33846509867

SN - 0944-6532

VL - 13

SP - 623

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JO - Journal of Convex Analysis

JF - Journal of Convex Analysis

IS - 3-4

ER -

There are many totally convex functions

Abstract

Keywords

ASJC Scopus subject areas

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