Convexity Properties Associated with Nonconvex Quadratic Matrix Functions and Applications to Quadratic Programming

A. Beck ()
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A. Beck: Technion–Israel Institute of Technology

Journal of Optimization Theory and Applications, 2009, vol. 142, issue 1, No 1, 29 pages

Abstract: Abstract We establish several convexity results which are concerned with nonconvex quadratic matrix (QM) functions: strong duality of quadratic matrix programming problems, convexity of the image of mappings comprised of several QM functions and existence of a corresponding S-lemma. As a consequence of our results, we prove that a class of quadratic problems involving several functions with similar matrix terms has a zero duality gap. We present applications to robust optimization, to solution of linear systems immune to implementation errors and to the problem of computing the Chebyshev center of an intersection of balls.

Keywords: Quadratic matrix functions; Strong duality; Extended S-lemma; Semidefinite relaxation; Convexity of quadratic maps (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/s10957-009-9539-y

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