Condition Number Theorems in Optimization
T. Zolezzi · SIAM Journal on Optimization · 2003
Condition numbers for optimization problems in Banach spaces are considered. Lower and upper estimates of the (suitably defined) distance from ill-conditioning are obtained in terms of the reciprocal of condition numbers. An approach is presented based on the metric regularity of the inverse to the arg min map. These results are extensions of the Eckart--Young distance theorem to optimization problems.