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설동렬,박순달,정호원 한국경영과학회 1996 한국경영과학회 학술대회논문집 Vol.- No.2
In Cholesky factorization of the interior point method, dense columns of A matrix make dense Cholesky factor L regardless of sparsity of A matrix. We introduce a method to tranform a primal problem to a dual problem in order to preserve the sparsity. KEYWORDS: Cholesky factorization, interior point method, dense column, sparsity, primal problem, dual problem
설동렬 한국경영과학회 2004 經營 科學 Vol.21 No.2
Every iteration of interior-point methods of large scale optimization requires computing at least one orthogonal projection. In the practice, symmetric variants of the Gaussian elimination such as Cholesky factorization are accepted as the most efficient and sufficiently stable method. In this paper several specific implementation issues of the symmetric factorization that can be applied for solving such equations are discussed. The code called McSML being the result of this work is shown to produce comparably sparse factors as another implementations in the MATLAB environment. It has been used for computing projections in an efficient implementation of self-regular based interior-point methods, McIPM. Although primary aim of developing McSML was to embed it into an interior-point methods optimizer, the code may equally well be used to solve general large sparse systems arising in different applications.