A Further Study on Asymptotic Functions via Variational Analysis

Felipe Lara; Rubén López; Benar F. Svaiter

doi:10.1007/s10957-019-01507-w

A Further Study on Asymptotic Functions via Variational Analysis

Felipe Lara
, Rubén López
, Benar F. Svaiter

Institute of Higher Research

Universidad de Tarapacá
Instituto National de Matemática Pura e Aplicada

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

5 Scopus citations

Abstract

We use variational analysis for studying asymptotic (recession or horizon) functions. We introduce the upper and lower asymptotic operators and study their domain and image. Moreover, we characterize their fixed points and zeros. Finally, we establish continuity properties of this operator, i.e., the convergence of asymptotic functions of convergent sequences of functions.

Original language	English
Pages (from-to)	366-382
Number of pages	17
Journal	Journal of Optimization Theory and Applications
Volume	182
Issue number	1
DOIs	https://doi.org/10.1007/s10957-019-01507-w
State	Published - Jul 2019

Keywords

Asymptotic functions
Epi-convergence
Operator theory
Set convergence
Variational analysis

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title = "A Further Study on Asymptotic Functions via Variational Analysis",

abstract = "We use variational analysis for studying asymptotic (recession or horizon) functions. We introduce the upper and lower asymptotic operators and study their domain and image. Moreover, we characterize their fixed points and zeros. Finally, we establish continuity properties of this operator, i.e., the convergence of asymptotic functions of convergent sequences of functions.",

keywords = "Asymptotic functions, Epi-convergence, Operator theory, Set convergence, Variational analysis",

author = "Felipe Lara and Rub{\'e}n L{\'o}pez and Svaiter, \{Benar F.\}",

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AU - Lara, Felipe

AU - López, Rubén

AU - Svaiter, Benar F.

N1 - Publisher Copyright: © Springer Science+Business Media, LLC, part of Springer Nature 2019

PY - 2019/7

Y1 - 2019/7

N2 - We use variational analysis for studying asymptotic (recession or horizon) functions. We introduce the upper and lower asymptotic operators and study their domain and image. Moreover, we characterize their fixed points and zeros. Finally, we establish continuity properties of this operator, i.e., the convergence of asymptotic functions of convergent sequences of functions.

AB - We use variational analysis for studying asymptotic (recession or horizon) functions. We introduce the upper and lower asymptotic operators and study their domain and image. Moreover, we characterize their fixed points and zeros. Finally, we establish continuity properties of this operator, i.e., the convergence of asymptotic functions of convergent sequences of functions.

KW - Asymptotic functions

KW - Epi-convergence

KW - Operator theory

KW - Set convergence

KW - Variational analysis

UR - https://www.scopus.com/pages/publications/85064184675

U2 - 10.1007/s10957-019-01507-w

DO - 10.1007/s10957-019-01507-w

M3 - Article

AN - SCOPUS:85064184675

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VL - 182

SP - 366

EP - 382

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 1

ER -

A Further Study on Asymptotic Functions via Variational Analysis

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Keywords

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