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On the Duality Gap in Nonconvex Optimization

Department of Mathematics, University of Pisa, Via Buonarroti 2, 56100 Pisa, Italy

Given a nonconvex constrained minimization problem, we introduce the dual problem by means of the ordinary Lagrangean function. The aim of the paper is to give, by means of the "image problem," an estimate of the duality gap using the definition of lack of convexity of a function.

Key Words: nonconvex optimization; duality; duality gap; Lagrangean function; image problem; lack of convexity