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Journal of Convex Analysis 26 (2019), No. 4, 1255--1276
Copyright Heldermann Verlag 2019

Zero-Scale Asymptotic Functions and Quasiconvex Optimization

Fabián Flores-Bazán
Dep. de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Chile

Nicolas Hadjisavvas
Dept. of Product and Systems Design Engineering, University of the Aegean, Hermoupolis, Syros, Greece
and: Mathematics and Statistics Department, King Fahd University of Petroleum and Minerals, Dhahran, Kingdom of Saudi Arabia

We introduce the notion of a zero-scale asymptotic function. In contrast to the usual asymptotic function, which is related to the slopes of a function at infinity along a given direction, the new function is related to the jumps of the function along that direction. Applications are given to the unconstrained and the constrained optimization of quasiconvex functions. Also, the problem of quasiconvex maximization is discussed. Further, a class of quasiconvex problems is introduced, that is shown to have zero duality gap. Finally, new results on quasiconvex quadratic programming are obtained.

Keywords: Asymptotic analysis, quasiconvexity, nonconvex optimization, quadratic optimization.

MSC: 90C30, 90C26

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