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ON CREATION OF SUPERNODES DURING ORDERING IN INTERIOR-POINT METHODS
Seol, Tongryeol,Park, Soondal 한국경영과학회 1998 Management Science and Financial Engineering Vol.4 No.1
Supernodes are used to exploit computer memory structures when Cholesky factorization is implemented in interior-point methods. Usually, supemodes are created after the fill-in reducing ordering. We introduce two new methods that create supernodes during ordering. The methods can save redundant computations during ordering, symbolic factorization and supernode creation. The first method consists of two steps. In the first step, we create supernodes form indistinguishable nodes during ordering. next, we enlarge them by applying post-order of the elimination tree and merging adjacent supernodes. In the second method, we create sufficiently enlarged supernodes, so-called maximal supernodes, directly during ordering. These are created from globally indistinguishable nodes. We define globally indistinguishable nodes by expanding the definition of the indistinguishable nodes.
내부점방법을 위한 초미디 열촐레스키 분해의 실험적 고찰
설동렬,정호원,박순달 한국경영과학회 1998 經營 科學 Vol.15 No.1
The computational speed of interior point method depends on the speed of Cholesky factorization. The supernodal column Cholesky factorization is a fast method that performs Cholesky factorization of sparse matrices with exploiting computer's characteristics. Three steps are necessary to perform the supernodal column Cholesky factorization: symbolic factorization, creation of the elimination tree, ordering by a post-order of the elimination tree and creation of supernodes. We study performing sequences of these three steps and efficient implementation of them.
설동렬,박찬규,서용원,박순달 한국경영과학회 1995 經營 科學 Vol.12 No.1
This paper is to develop an integrated environment software on MS-DOS for linear programming. For the purpose, First, the linear programming integrated environment software satisfying both the educational purpose and the professional purpose was designed and constructed on MS-DOS. Second, the text editor with big capacity was developed. The arithmetic form analyser was also developed and connected to the text editor so that users can input data in the arithmetic form. As a result, users can learn and perform linear programming in the linear programming integrated environment software.
설동렬,박순달,정호원 한국경영과학회 1997 經營 科學 Vol.14 No.2
The computational speed of interior point method of linear programming depends on the speed of Cholesky factorization. If the coefficient matrix A has dense columns then the matrix A??A^T becomes a dense matrix. This causes Cholesky factorization to be slow. We study an efficient implementation method of the dense column splitting among dense column resolving techniques and analyze the relation between dense column splitting and ordering methods to improve the sparsity of Cholesky factor.
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.