Optimization Letters

, Volume 7, Issue 5, pp 903–911

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

Authors

    • Faculty of InformaticsUniversity of Debrecen
    • Department of MathematicsTU Berlin
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).

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© Springer-Verlag 2012