General-purpose preconditioning for regularized interior point methods
General-purpose preconditioning for regularized interior point methods
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DOI：
10.1007/s10589-022-00424-5
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发表时间：
2021-07
影响因子：
2.2
通讯作者：
J. Gondzio;Spyridon Pougkakiotis;J. Pearson
中科院分区：
文献类型：
--
作者：
J. Gondzio;Spyridon Pougkakiotis;J. Pearson
在本文中，我们提出了通用的正则增广系统的预条件，以及相应的正规方程，所产生的优化问题。我们讨论了正定预条件子，适用于CG和MINRES。我们认为“稀疏化”，避免的情况下，预处理矩阵的特征值可能会变得复杂。特别注意的是系统所产生的应用程序的正则化内点方法的线性或非线性凸规划问题。
In this paper we present general-purpose preconditioners for regularized augmented systems, and their corresponding normal equations, arising from optimization problems. We discuss positive definite preconditioners, suitable for CG and MINRES. We consider “sparsifications" which avoid situations in which eigenvalues of the preconditioned matrix may become complex. Special attention is given to systems arising from the application of regularized interior point methods to linear or nonlinear convex programming problems.