Optimization Letters

, Volume 7, Issue 5, pp 903–911

Necessary and sufficient condition on global optimality without convexity and second order differentiability

Original Paper

DOI: 10.1007/s11590-012-0465-9

Cite this article as:
Burai, P. Optim Lett (2013) 7: 903. doi:10.1007/s11590-012-0465-9

Abstract

The main goal of this paper is to give a necessary and sufficient condition of global optimality for unconstrained optimization problems, when the objective function is not necessarily convex. We use Gâteaux differentiability of the objective function and its bidual (the latter is known from convex analysis).

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Faculty of InformaticsUniversity of DebrecenDebrecenHungary
  2. 2.Department of MathematicsTU BerlinBerlinGermany