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A sharp Lagrange multiplier theorem for nonlinear programs

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  • M. Ruiz Galán

    (University of Granada)

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.

Suggested Citation

  • M. Ruiz Galán, 2016. "A sharp Lagrange multiplier theorem for nonlinear programs," Journal of Global Optimization, Springer, vol. 65(3), pages 513-530, July.
    • Handle: RePEc:spr:jglopt:v:65:y:2016:i:3:d:10.1007_s10898-015-0379-z
    DOI: 10.1007/s10898-015-0379-z
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    References listed on IDEAS

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    1. Nguyen Huy Chieu & Gue Myung Lee, 2014. "Constraint Qualifications for Mathematical Programs with Equilibrium Constraints and their Local Preservation Property," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 755-776, December.
    2. T. Illés & G. Kassay, 1999. "Theorems of the Alternative and Optimality Conditions for Convexlike and General Convexlike Programming," Journal of Optimization Theory and Applications, Springer, vol. 101(2), pages 243-257, May.
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