Iterative Methods for Equality-Constrained Least Squares Problems

Barlow, J. L., Nichols, N. ORCID: https://orcid.org/0000-0003-1133-5220 and Plemmons, R. J. (1988) Iterative Methods for Equality-Constrained Least Squares Problems. SIAM Journal on Scientific and Statistical Computing, 9 (5). pp. 892-906. ISSN 0196-5204 doi: 10.1137/0909061

Abstract/Summary

We consider the linear equality-constrained least squares problem (LSE) of minimizing ${\|c - Gx\|}_2 $, subject to the constraint $Ex = p$. A preconditioned conjugate gradient method is applied to the Kuhn–Tucker equations associated with the LSE problem. We show that our method is well suited for structural optimization problems in reliability analysis and optimal design. Numerical tests are performed on an Alliant FX/8 multiprocessor and a Cray-X-MP using some practical structural analysis data.