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Journal of Convex Analysis 09 (2002), No. 2, 693--700
Copyright Heldermann Verlag 2002



On the Distance Theorem in Quadratic Optimization

T. Zolezzi
Dip. di Matematica, UniversitÓ di Genova, Via Dodecaneso 35, 16146 Genova, Italy
zolezzi@dima.unige.it



The optimization of convex quadratic forms on Banach spaces is considered. A suitable notion of conditioning under linear perturbations leads to the distance theorem in the free case, thereby extending to the optimization setting the classical Eckart-Young formula: the distance to ill-conditioning equals to the reciprocal of the condition number. Partial results are presented for the linearly constrained case.

Keywords: Conditioning, distance theorem, condition number theorem, convex optimization.

MSC: 49K40

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