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 email@example.com Felipe Lara firstname.lastname@example.org Juan Enrique Martínez-Legaz email@example.com 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 of Optimization Theory and Applications – Springer Journals
Published: Jun 4, 2018
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