First- and Second-Order Asymptotic Analysis with Applications in Quasiconvex Optimization

F. Flores-Bazán (), N. Hadjisavvas, F. Lara and I. Montenegro
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F. Flores-Bazán: Universidad de Concepción
N. Hadjisavvas: King Fahd University of Petroleum and Minerals
F. Lara: Universidad de Tarapacá
I. Montenegro: Universidad de Concepción

Journal of Optimization Theory and Applications, 2016, vol. 170, issue 2, No 3, 372-393

Abstract: Abstract We use asymptotic analysis to describe in a more systematic way the behavior at the infinity of functions in the convex and quasiconvex case. Starting from the formulae for the first- and second-order asymptotic function in the convex case, we introduce similar notions suitable for dealing with quasiconvex functions. Afterward, by using such notions, a class of quasiconvex vector mappings under which the image of a closed convex set is closed, is introduced; we characterize the nonemptiness and boundedness of the set of minimizers of any lsc quasiconvex function; finally, we also characterize boundedness from below, along lines, of any proper and lsc function.

Keywords: Quasiconvexity; Asymptotic functions; Second-order asymptotic functions and cones; Optimality conditions; Nonconvex optimization; 90C26; 90C30 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-016-0938-6

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