UPPER PERTURBATION BOUNDS OF WEIGHTED PROJECTIONS, WEIGHTED AND CONSTRAINED LEAST SQUARES PROBLEMS.

At each iteration step for solving mathematical programming and constrained optimization problems by using interior-point methods, one often needs to solve the weighted least squares (WLS) problem min_x∈Rn ¦¦W½(Ax - b)¦¦, or the weighted and constrained least squares (WLSE) problem min_x∈Rn ¦¦W½(Kx - g)¦¦ subject to Lx = h, where W = diag(w₁,…,w_l) > 0 in which some w_i → +∝ and some w_i → 0. In this paper we will derive upper perturbation bounds of weighted projections associated with the WLS and WLSE problems when W ranges over the set D of positive diagonal matrices. We then apply these bounds to deduce upper perturbation bounds of solutions of WLS and WLSE problems when W ranges over D. We also extend the estimates to the cases when W ranges over a subset of real symmetric positive semidefinite matrices. [ABSTRACT FROM AUTHOR]