Journal of Convex Analysis 22 (2015), No. 4, 1173--1196
Copyright Heldermann Verlag 2015
Second Order Asymptotic Analysis: Basic Theory
Fabián Flores-Bazán
Dep. de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile
fflores@ing-mat.udec.cl
Nicolas Hadjisavvas
Mathematics and Statistics Department, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
nhadjisavvas@gmail.com
Felipe Lara
Dep. de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile
felipelara@udec.cl
Recently, the concepts of second order asymptotic directions and functions have been introduced and applied to global and vector optimization problems. In this work, we establish some new properties for these two concepts. In particular, in case of a convex set, a complete characterization of the second order asymptotic cone is given. Also, formulas that permit the easy computation of the second order asymptotic function of a convex function are established. It is shown that the second order asymptotic function provides a finer description of the behavior of functions at infinity, than the first order asymptotic function. Finally, we show that second order asymptotic function of a given convex one can be seen as first order asymptotic function of another convex function.
Keywords: Asymptotic cone, recession cone, asymptotic function, second order asymptotic cone, second order asymptotic function.
[ Fulltext-pdf (200 KB)] for subscribers only.