Maximizing Strictly Convex Quadratic Functions withBounded Perturbations

The problem of maximizing 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,+ infinity [. The location of global maximal solutions of f ~ on D is derived from the roug...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2011-04, Vol.149 (1), p.1-25
Main Authors: Phu, H X, Pho, V M, An, P T
Format: Article
Language:English
Subjects:
Convexity
Optimization
Perturbation methods
Position (location)
Upper bounds
Online Access:Get full text
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Summary:The problem of maximizing 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,+ infinity [. The location of global maximal solutions of f ~ on D is derived from the roughly generalized convexity of f ~ . The distance between global (or local) maximal solutions of 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 f ~ on D is upper (or lower, respectively) semicontinuous when the upper bound s tends to zero.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-010-9772-4