SOLVING LINEAR-SYSTEMS INVOLVED IN CONSTRAINED OPTIMIZATION

作     者：SHI, YX 

作者机构：Department of Mathematics & Computer Science Bloomsburg University of Pennsylvania Bloomsburg Pennsylvania 17815 USA 

出 版 物：《LINEAR ALGEBRA AND ITS APPLICATIONS》 (线性代数及其应用)

年 卷 期：1995年第229卷第C期

页      面：175-189页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

摘      要：Many interior point methods for large scale linear programming, quadratic programming, the convex programming solve an (n + m) x (n + m) linear system in each iteration. The last m equations require exact solutions in order to maintain the feasibility. Current implementations reduce that step to solving an m x m linear system. The solution must be exact, because otherwise the error would be entirely passed on to the last m equations of the original system. This makes the computation costly and sometimes impractical. In this paper, we propose an inexpensive iterative method for solving that (n + m) x (n + m) system. It guarantees exact solutions to the last m equations. The convergence is proved, and the implementational issues are discussed. Some preliminary numerical results are also reported.