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Global infimum of strictly convex quadratic functions with bounded perturbations

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  • Hoang Phu
  • Vo Pho

Abstract

The problem of minimizing $${\tilde f=f+p}$$ over some convex subset of a Euclidean space is investigated, where f(x) = x T Ax + b T x is strictly convex and |p| is only assumed to be bounded by some positive number s. It is shown that the function $${\tilde f}$$ is strictly outer γ-convex for any γ > γ*, where γ* is determined by s and the smallest eigenvalue of A. As consequence, a γ*-local minimal solution of $${\tilde f}$$ is its global minimal solution and the diameter of the set of global minimal solutions of $${\tilde f}$$ is less than or equal to γ*. Especially, the distance between the global minimal solution of f and any global minimal solution of $${\tilde f}$$ is less than or equal to γ*/2. This property is used to prove a roughly generalized support property of $${\tilde f}$$ and some generalized optimality conditions. Copyright Springer-Verlag 2010

Suggested Citation

  • Hoang Phu & Vo Pho, 2010. "Global infimum of strictly convex quadratic functions with bounded perturbations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(2), pages 327-345, October.
  • Handle: RePEc:spr:mathme:v:72:y:2010:i:2:p:327-345
    DOI: 10.1007/s00186-010-0324-3
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    Cited by:

    1. H. X. Phu & V. M. Pho & P. T. An, 2011. "Maximizing Strictly Convex Quadratic Functions with Bounded Perturbations," Journal of Optimization Theory and Applications, Springer, vol. 149(1), pages 1-25, April.

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