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Semi-continuous quadratic optimization: existence conditions and duality scheme

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  • John Cotrina
  • Fernanda Raupp
  • Wilfredo Sosa

Abstract

In this work, we study the class of problems called semi-continuous optimization, which contains constrained minimization (maximization) problems with lower (upper) semi-continuous objective functions. We show some existence conditions for solutions based on asymptotic techniques, as well as a duality scheme based on the Fenchel–Moreau conjugation specifically applied to semi-continuous problems. Promising results are obtained, when we apply this scheme to minimize quadratic functions (whose Hessians can be symmetric indefinite) over nonempty, closed and convex polyhedral sets. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • John Cotrina & Fernanda Raupp & Wilfredo Sosa, 2015. "Semi-continuous quadratic optimization: existence conditions and duality scheme," Journal of Global Optimization, Springer, vol. 63(2), pages 281-295, October.
    • Handle: RePEc:spr:jglopt:v:63:y:2015:i:2:p:281-295
    DOI: 10.1007/s10898-015-0306-3
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    References listed on IDEAS

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    1. Alfred Auslender, 1996. "Noncoercive Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 21(4), pages 769-782, November.
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    Cited by:

    1. Tran Nghi & Nguyen Nang Tam, 2020. "A Frank–Wolfe-Type Theorem for Cubic Programs and Solvability for Quadratic Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 448-468, November.
    2. F. Flores-Bazán & N. Hadjisavvas & F. Lara & I. Montenegro, 2016. "First- and Second-Order Asymptotic Analysis with Applications in Quasiconvex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 372-393, August.

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