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Maximizing Strictly Convex Quadratic Functions with Bounded Perturbations

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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.

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Authors and Affiliations

  1. Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam

    H. X. Phu & P. T. An

  2. Faculty of Information Technology, Le Qui Don University, Hanoi, Vietnam

    V. M. Pho

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  1. H. X. Phu
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  2. V. M. Pho
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  3. P. T. An
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Correspondence to H. X. Phu.

Additional information

Communicated by Boris Mordukhovich.

This work was supported by Vietnam National Foundation for Science and Technology Development.

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Phu, H.X., Pho, V.M. & An, P.T. Maximizing Strictly Convex Quadratic Functions with Bounded Perturbations. J Optim Theory Appl 149, 1–25 (2011). https://doi.org/10.1007/s10957-010-9772-4

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