Abstract

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.

Author information

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

Fabián Flores-Bazán

Dep. de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Chile

fflores@ing-mat.udec.cl

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

nhad@aegean.gr

Keywords

  • Asymptotic analysis
  • quasiconvexity
  • nonconvex optimization
  • quadratic optimization

Mathematics Subject Classification

90C30, 90C26

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Suggested citation

F. Flores-Bazán, N. Hadjisavvas. “Zero-Scale Asymptotic Functions and Quasiconvex Optimization.” Journal of Convex Analysis 26 (2019), No. 4, 1255–1276. https://doi.org/10.68381/jca26066

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Published by Heldermann Verlag, 2019. Rights now held by Banach Press LLC.