A Quasiconvex Asymptotic Function with Applications in Optimization

A Quasiconvex Asymptotic Function with Applications in Optimization J Optim Theory Appl https://doi.org/10.1007/s10957-018-1317-2 A Quasiconvex Asymptotic Function with Applications in Optimization 1,2 3 Nicolas Hadjisavvas · Felipe Lara · 4,5 Juan Enrique Martínez-Legaz Received: 2 March 2018 / Accepted: 17 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract We introduce a new asymptotic function, which is mainly adapted to qua- siconvex 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. Keywords Asymptotic cones · Asymptotic functions · Quasiconvexity · Nonconvex optimization · Closedness criteria Mathematics Subject Classification 90C25 · 90C26 · 90C30 Nicolas Hadjisavvas nhad@aegean.gr Felipe Lara felipelaraobreque@gmail.com Juan Enrique Martínez-Legaz juanenrique.martinez.legaz@uab.cat Department of Product and Systems Design Engineering, University of the Aegean, Hermoúpolis, Syros, Greece Mathematics and Statistics Department, King Fahd University of Petroleum and Minerals, Dhahran, Kingdom of Saudi Arabia Departamento de Matemáticas, Universidad de Tarapacá, Arica, Chile http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Optimization Theory and Applications Springer Journals

A Quasiconvex Asymptotic Function with Applications in Optimization

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Publisher
Springer US
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory
ISSN
0022-3239
eISSN
1573-2878
D.O.I.
10.1007/s10957-018-1317-2
Publisher site
See Article on Publisher Site

Abstract

J Optim Theory Appl https://doi.org/10.1007/s10957-018-1317-2 A Quasiconvex Asymptotic Function with Applications in Optimization 1,2 3 Nicolas Hadjisavvas · Felipe Lara · 4,5 Juan Enrique Martínez-Legaz Received: 2 March 2018 / Accepted: 17 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract We introduce a new asymptotic function, which is mainly adapted to qua- siconvex 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. Keywords Asymptotic cones · Asymptotic functions · Quasiconvexity · Nonconvex optimization · Closedness criteria Mathematics Subject Classification 90C25 · 90C26 · 90C30 Nicolas Hadjisavvas nhad@aegean.gr Felipe Lara felipelaraobreque@gmail.com Juan Enrique Martínez-Legaz juanenrique.martinez.legaz@uab.cat Department of Product and Systems Design Engineering, University of the Aegean, Hermoúpolis, Syros, Greece Mathematics and Statistics Department, King Fahd University of Petroleum and Minerals, Dhahran, Kingdom of Saudi Arabia Departamento de Matemáticas, Universidad de Tarapacá, Arica, Chile

Journal

Journal of Optimization Theory and ApplicationsSpringer Journals

Published: Jun 4, 2018

References

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