A sharp Lagrange multiplier theorem for nonlinear programs

M. Ruiz Galán ()
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M. Ruiz Galán: University of Granada

Journal of Global Optimization, 2016, vol. 65, issue 3, No 5, 513-530

Abstract: Abstract For a nonlinear program with inequalities and under a Slater constraint qualification, it is shown that the duality between optimal solutions and saddle points for the corresponding Lagrangian is equivalent to the infsup-convexity—a not very restrictive generalization of convexity which arises naturally in minimax theory—of a finite family of suitable functions. Even if we dispense with the Slater condition, it is proven that the infsup-convexity is nothing more than an equivalent reformulation of the Fritz John conditions for the nonlinear optimization problem under consideration.

Keywords: Nonlinear programming; Lagrange multipliers; Infsup-convexity; Separation theorem; Karush–Kuhn–Tucker conditions; Fritz John conditions; 90C30; 90C46; 26B25; 46A22 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10898-015-0379-z

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