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A theorem of the alternative with an arbitrary number of inequalities and quadratic programming

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  • M. Ruiz Galán

    (University of Granada)

Abstract

In this paper we are concerned with a Gordan-type theorem involving an arbitrary number of inequality functions. We not only state its validity under a weak convexity assumption on the functions, but also show it is an optimal result. We discuss generalizations of several recent results on nonlinear quadratic optimization, as well as a formula for the Fenchel conjugate of the supremum of a family of functions, in order to illustrate the applicability of that theorem of the alternative.

Suggested Citation

  • M. Ruiz Galán, 2017. "A theorem of the alternative with an arbitrary number of inequalities and quadratic programming," Journal of Global Optimization, Springer, vol. 69(2), pages 427-442, October.
    • Handle: RePEc:spr:jglopt:v:69:y:2017:i:2:d:10.1007_s10898-017-0525-x
    DOI: 10.1007/s10898-017-0525-x
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    References listed on IDEAS

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    1. A. Dax & V. P. Sreedharan, 1997. "Theorems of the Alternative and Duality," Journal of Optimization Theory and Applications, Springer, vol. 94(3), pages 561-590, September.
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    6. Sheng-Long Hu & Zheng-Hai Huang, 2012. "Theorems of the Alternative for Inequality Systems of Real Polynomials," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 1-16, July.
    7. Ziyan Luo & Linxia Qin & Lingchen Kong & Naihua Xiu, 2014. "The Nonnegative Zero-Norm Minimization Under Generalized Z-Matrix Measurement," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 854-864, March.
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