Original Paper

Optimization Letters

, Volume 7, Issue 5, pp 903-911

First online:

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

  • Pál BuraiAffiliated withFaculty of Informatics, University of DebrecenDepartment of Mathematics, TU Berlin Email author 

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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).