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

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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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Authors and Affiliations

  1. Faculty of Informatics, University of Debrecen, Pf. 12, Debrecen, 4010, Hungary

    Pál Burai

  2. Department of Mathematics, TU Berlin, Strae des 17. Juni 136, 10623, Berlin, Germany

    Pál Burai

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  1. Pál Burai
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Correspondence to Pál Burai.

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Burai, P. Necessary and sufficient condition on global optimality without convexity and second order differentiability. Optim Lett 7, 903–911 (2013). https://doi.org/10.1007/s11590-012-0465-9

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  • DOI: https://doi.org/10.1007/s11590-012-0465-9

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