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, Università 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
[ Fulltext-pdf (206 KB)]