A Quasiconvex Asymptotic Function with Applications in Optimization

Nicolas Hadjisavvas; Felipe Lara; Juan Enrique Martínez-Legaz

doi:10.1007/s10957-018-1317-2

A Quasiconvex Asymptotic Function with Applications in Optimization

Nicolas Hadjisavvas, Felipe Lara, Juan Enrique Martínez-Legaz

Department of Economics and Economic History

Research output: Contribution to journal › Article › Research

8 Citations (Scopus)

Abstract

© 2018, Springer Science+Business Media, LLC, part of Springer Nature. We introduce a new asymptotic function, which is mainly adapted to quasiconvex functions. We establish several properties and calculus rules for this concept and compare it to previous notions of generalized asymptotic functions. Finally, we apply our new definition to quasiconvex optimization problems: we characterize the boundedness of the function, and the nonemptiness and compactness of the set of minimizers. We also provide a sufficient condition for the closedness of the image of a nonempty closed and convex set via a vector-valued function.

Original language	English
Pages (from-to)	170-186
Journal	Journal of Optimization Theory and Applications
Volume	180
DOIs	https://doi.org/10.1007/s10957-018-1317-2
Publication status	Published - 15 Jan 2019

Keywords

Asymptotic cones
Asymptotic functions
Closedness criteria
Nonconvex optimization
Quasiconvexity

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title = "A Quasiconvex Asymptotic Function with Applications in Optimization",

abstract = "{\textcopyright} 2018, Springer Science+Business Media, LLC, part of Springer Nature. We introduce a new asymptotic function, which is mainly adapted to quasiconvex functions. We establish several properties and calculus rules for this concept and compare it to previous notions of generalized asymptotic functions. Finally, we apply our new definition to quasiconvex optimization problems: we characterize the boundedness of the function, and the nonemptiness and compactness of the set of minimizers. We also provide a sufficient condition for the closedness of the image of a nonempty closed and convex set via a vector-valued function.",

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author = "Nicolas Hadjisavvas and Felipe Lara and Mart{\'i}nez-Legaz, {Juan Enrique}",

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AU - Hadjisavvas, Nicolas

AU - Lara, Felipe

AU - Martínez-Legaz, Juan Enrique

PY - 2019/1/15

Y1 - 2019/1/15

N2 - © 2018, Springer Science+Business Media, LLC, part of Springer Nature. We introduce a new asymptotic function, which is mainly adapted to quasiconvex functions. We establish several properties and calculus rules for this concept and compare it to previous notions of generalized asymptotic functions. Finally, we apply our new definition to quasiconvex optimization problems: we characterize the boundedness of the function, and the nonemptiness and compactness of the set of minimizers. We also provide a sufficient condition for the closedness of the image of a nonempty closed and convex set via a vector-valued function.

AB - © 2018, Springer Science+Business Media, LLC, part of Springer Nature. We introduce a new asymptotic function, which is mainly adapted to quasiconvex functions. We establish several properties and calculus rules for this concept and compare it to previous notions of generalized asymptotic functions. Finally, we apply our new definition to quasiconvex optimization problems: we characterize the boundedness of the function, and the nonemptiness and compactness of the set of minimizers. We also provide a sufficient condition for the closedness of the image of a nonempty closed and convex set via a vector-valued function.

KW - Asymptotic cones

KW - Asymptotic functions

KW - Closedness criteria

KW - Nonconvex optimization

KW - Quasiconvexity

U2 - 10.1007/s10957-018-1317-2

DO - 10.1007/s10957-018-1317-2

M3 - Article

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SP - 170

EP - 186

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

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