A Quasiconvex Asymptotic Function with Applications in Optimization

Nicolas Hadjisavvas (), Felipe Lara () and Juan Enrique Martinez-Legaz
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Nicolas Hadjisavvas: University of the Aegean
Felipe Lara: Universidad de Tarapacá

Journal of Optimization Theory and Applications, 2019, vol. 180, issue 1, No 10, 170-186

Abstract: Abstract 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.

Keywords: Asymptotic cones; Asymptotic functions; Quasiconvexity; Nonconvex optimization; Closedness criteria; 90C25; 90C26; 90C30 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-018-1317-2

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