Maximizing Strictly Convex Quadratic Functions with Bounded Perturbations

  • H. X. PhuEmail author
  • V. M. Pho
  • P. T. An


The problem of maximizing \(\tilde{f}=f+p\) over some convex subset D of the n-dimensional Euclidean space is investigated, where f is a strictly convex quadratic function and p is assumed to be bounded by some s∈[0,+∞[. The location of global maximal solutions of \(\tilde{f}\) on D is derived from the roughly generalized convexity of \(\tilde{f}\). The distance between global (or local) maximal solutions of \(\tilde{f}\) on D and global (or local, respectively) maximal solutions of f on D is estimated. As consequence, the set of global (or local) maximal solutions of \(\tilde{f}\) on D is upper (or lower, respectively) semicontinuous when the upper bound s tends to zero.


Quadratic function Convex maximization Generalized convexity Bounded perturbation Stability 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam
  2. 2.Faculty of Information TechnologyLe Qui Don UniversityHanoiVietnam

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