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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

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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