Incomplete orthogonalization preconditioners for solving large and dense linear systems which arise from Semidefinite Programming

Abstract

There is a strong need for the fast solution of large and dense linear systems which arise from the interior-point method for solving Semidefinite Programming with its dual problem. Often direct methods are too expensive in terms of computer memory and CPU-time requirements, then the only alternative is to use iterative methods. Here, a class of incomplete orthogonalization preconditioners for the conjugate gradient method for solving this type of linear systems will be proposed. The efficient feature of the preconditioners will be confirmed by several numerical experiments.