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Stable Reduction to KKT Systems in Barrier Methods for Linear and Quadratic Programming

Stanford University. Engineering-Economic Systems and Operations Research Department. Systems Optimization LaboratoryThomas J. Watson IBM Research CenterMichael A. SaundersJohn A. Tomlin

出版	IBM Thomas J. Watson Research Division, 1996
URL	http://books.google.com.hk/books?id=qdYHAAAAIAAJ&hl=&source=gbs_api

註釋Abstract: "We discuss methods for solving the key linear equations within primal-dual barrier methods for linear and quadratic programming. Following Freund and Jarre, we explore methods for reducing the Newton equations to 2 X 2 block systems (KKT systems) in a stable manner. Some methods require partitioning the variables into two or more parts, but a simpler approach is derived and recommended. To justify symmetrizing the KKT systems, we assume the use of a sparse solver whose numerical properties are independent of row and column scaling. In particular, we regularize the problem and use indefinite Cholesky-type factorizations. An implementation within OSL is tested on the larger NETLIB examples."