等式约束最小二乘问题的迭代方法

Siam Journal on Scientific and Statistical Computing Pub Date : 1988-09-01 DOI:10.1137/0909061

J. Barlow, N. Nichols, R. Plemmons

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引用次数: 41

摘要

考虑在$Ex = p$约束下，使${\|c - Gx\|}_2 $最小化的线性等约束最小二乘问题。将预条件共轭梯度法应用于LSE问题相关的Kuhn-Tucker方程。结果表明，该方法适用于可靠性分析和优化设计中的结构优化问题。利用一些实际的结构分析数据，在Alliant FX/8多处理器和Cray-X-MP上进行了数值测试。

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Iterative Methods for Equality-Constrained Least Squares Problems

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.

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Siam Journal on Scientific and Statistical Computing

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