The q-asymptotic function in c-convex analysis

A. Iusem; F. Lara

doi:10.1080/02331934.2018.1456540

The q-asymptotic function in c-convex analysis

A. Iusem
, F. Lara

Institute of Higher Research

Instituto National de Matemática Pura e Aplicada

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

7 Scopus citations

Abstract

We establish several connections between generalized asymptotic functions and different areas of convexity theory, without coercivity assumptions. Properties and characterizations of abstract subdifferentials, normal cones, conjugates, support functions and optimality conditions for the minimization problem are given. We provide a new result on existence of minimizers for a class of nonconvex functions which is strictly larger than the class of quasiconvex ones.

Original language	English
Pages (from-to)	1429-1445
Number of pages	17
Journal	Optimization
Volume	68
Issue number	7
DOIs	https://doi.org/10.1080/02331934.2018.1456540
State	Published - 3 Jul 2019

Keywords

Asymptotic functions
conjugacies
generalized convexity
optimality conditions
subdifferentials
support functions

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10.1080/02331934.2018.1456540

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AB - We establish several connections between generalized asymptotic functions and different areas of convexity theory, without coercivity assumptions. Properties and characterizations of abstract subdifferentials, normal cones, conjugates, support functions and optimality conditions for the minimization problem are given. We provide a new result on existence of minimizers for a class of nonconvex functions which is strictly larger than the class of quasiconvex ones.

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KW - conjugacies

KW - generalized convexity

KW - optimality conditions

KW - subdifferentials

KW - support functions

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The q-asymptotic function in c-convex analysis

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Keywords

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