Geodesic
On the Distance Theorem in Quadratic Optimization
Journal of convex analysis, Tome 9 (2002) no. 2, pp. 693-7.

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 49K40
Mots-clés : Conditioning, distance theorem, condition number theorem, convex optimization 
@article{JCA_2002_9_2_JCA_2002_9_2_a21,
     author = {T. Zolezzi},
     title = {On the {Distance} {Theorem} in {Quadratic} {Optimization}},
     journal = {Journal of convex analysis},
     pages = {693--7},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2002},
     url = {http://geodesic.mathdoc.fr/item/JCA_2002_9_2_JCA_2002_9_2_a21/}
}
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T. Zolezzi. On the Distance Theorem in Quadratic Optimization. Journal of convex analysis, Tome 9 (2002) no. 2, pp. 693-7. http://geodesic.mathdoc.fr/item/JCA_2002_9_2_JCA_2002_9_2_a21/