Maximizing Strictly Convex Quadratic Functions with Bounded Perturbations

H. X. Phu (), V. M. Pho () and P. T. An ()
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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

Journal of Optimization Theory and Applications, 2011, vol. 149, issue 1, No 1, 25 pages

Abstract: 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.

Keywords: Quadratic function; Convex maximization; Generalized convexity; Bounded perturbation; Stability (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10957-010-9772-4

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