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UPPER PERTURBATION BOUNDS OF WEIGHTED PROJECTIONS, WEIGHTED AND CONSTRAINED LEAST SQUARES PROBLEMS.
- Source :
- SIAM Journal on Matrix Analysis & Applications; 2000, Vol. 21 Issue 3, p931-951, 21p
- Publication Year :
- 2000
-
Abstract
- 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<subscript>x∈Rn</subscript> ¦¦W½(Ax - b)¦¦, or the weighted and constrained least squares (WLSE) problem min<subscript>x∈Rn</subscript> ¦¦W½(Kx - g)¦¦ subject to Lx = h, where W = diag(w<subscript>1</subscript>,…,w<subscript>l</subscript>) > 0 in which some w<subscript>i</subscript> → +∝ and some w<subscript>i</subscript> → 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]
Details
- Language :
- English
- ISSN :
- 08954798
- Volume :
- 21
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- SIAM Journal on Matrix Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 13213927
- Full Text :
- https://doi.org/10.1137/S0895479898336306