Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Asymptotic cone
  • recession cone
  • asymptotic function
  • second order asymptotic cone
  • second order asymptotic function

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Suggested citation

F. Flores-Bazán, N. Hadjisavvas, F. Lara. “Second Order Asymptotic Analysis: Basic Theory.” Journal of Convex Analysis 22 (2015), No. 4, 1173–1196. https://doi.org/10.68381/jca22061

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Published by Heldermann Verlag, 2015. Rights now held by Banach Press LLC.