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Maximizing Strictly Convex Quadratic Functions with Bounded Perturbations

Author

Listed:
  • H. X. Phu

    (Vietnam Academy of Science and Technology)

  • V. M. Pho

    (Le Qui Don University)

  • P. T. An

    (Vietnam Academy of Science and Technology)

Abstract

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.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:149:y:2011:i:1:d:10.1007_s10957-010-9772-4
    DOI: 10.1007/s10957-010-9772-4
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