The cholesky factorization in interior point methods

Y-MP Floating Point and Cholesky Factorization

Introduction The Cray 2 and Cray Y-MP are in many respects very similar computer systems, particularly when compared with other computer systems currently available. This similarity extends to the area of floating point arithmetic hardware implementation. The hardware implementations differ only very slightly, but this difference is sufficient to cause certain algorithms to exhibit significant ...

Modified Cholesky Factorizations in Interior-Point Algorithms for Linear Programming

We investigate a modi ed Cholesky algorithm typical of those used in most interiorpoint codes for linear programming. Cholesky-based interior-point codes are popular for three reasons: their implementation requires only minimal changes to standard sparse Cholesky algorithms (allowing us to take full advantage of software written by specialists in that area); they tend to be more e cient than co...

Cholesky factorization

This article aimed at a general audience of computational scientists, surveys the Cholesky factorization for symmetric positive definite matrices, covering algorithms for computing it, the numerical stability of the algorithms, and updating and downdating of the factorization. Cholesky factorization with pivoting for semidefinite matrices is also treated.  2009 John Wiley & Sons, Inc. WIREs Co...

Interior-point Methods

Interior-Point Methods

The modern era of interior-point methods dates to 1984, when Karmarkar proposed his algorithm for linear programming. In the years since then, algorithms and software for linear programming have become quite sophisticated, while extensions to more general classes of problems, such as convex quadratic programming, semide nite programming, and nonconvex and nonlinear problems, have reached varyin...