Approximation of quasiconvex functions by neatly quasiconvex functions

Suliman Al-Homidan; Loai Shaalan

doi:10.1007/s11590-020-01535-w

Approximation of quasiconvex functions by neatly quasiconvex functions

Suliman Al-Homidan, Loai Shaalan^*

^*Corresponding author for this work

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

1 Scopus citations

Abstract

A local minimum of a quasiconvex function is not necessarily a global minimum. In this paper, we show that every lower semicontinuous quasiconvex function can be approximated uniformly by a sequence of quasiconvex functions for which every local minimum is a global minimum. We also study the continuity of the functions appearing in a recently obtained decomposition of quasiconvex functions.

Original language	English
Pages (from-to)	979-989
Number of pages	11
Journal	Optimization Letters
Volume	15
Issue number	3
DOIs	https://doi.org/10.1007/s11590-020-01535-w
State	Published - Apr 2021

Bibliographical note

Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.

Keywords

Adjusted sublevel sets
Neatly quasiconvex function
Quasiconvex function
Quasiconvex optimization

ASJC Scopus subject areas

Control and Optimization

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10.1007/s11590-020-01535-w

Cite this

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abstract = "A local minimum of a quasiconvex function is not necessarily a global minimum. In this paper, we show that every lower semicontinuous quasiconvex function can be approximated uniformly by a sequence of quasiconvex functions for which every local minimum is a global minimum. We also study the continuity of the functions appearing in a recently obtained decomposition of quasiconvex functions.",

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AB - A local minimum of a quasiconvex function is not necessarily a global minimum. In this paper, we show that every lower semicontinuous quasiconvex function can be approximated uniformly by a sequence of quasiconvex functions for which every local minimum is a global minimum. We also study the continuity of the functions appearing in a recently obtained decomposition of quasiconvex functions.

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KW - Quasiconvex function

KW - Quasiconvex optimization

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Approximation of quasiconvex functions by neatly quasiconvex functions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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