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성명기,임성묵,박순달 한국경영과학회 1999 韓國經營科學會誌 Vol.24 No.1
We classified preprocessing methods into (1) analytic methods. (20 methods for removing implied free variables, (3) methods using pivot or elementary row operations. (4) methods for removing linearly dependent rows and columns and (5) methods for dense columns We noted some considerations to which should be paid attention when preprocessing methods are applied to interior point methods for linear programming we proposed an efficient order of preprocessing methods and data structures We also noted the recovery process for dual solutions We implemented the proposed preprocessing methods, and tested it with 28 large scale problems of NETLIB We compared the results of it with those of preprocessing routines of HOPDM, BPDPM and CPLEX
내부점 방법에서 Augmented System의 촐레스키 분해
도승용,성명기,박순달 한국경영과학회 2003 한국경영과학회지 Vol.28 No.1
In the normal equations approach in which the ordering and factorization phases are separated, the factorization in the augmented system approach is computed dynamically. This means that in the augmented system the numerical factorization should be performed to obtain the non-zero structure of Cholesky factor L. This causes much time to set up the non-zero structure of Cholesky factor L. So we present a method which can separate the ordering and numerical factorization in the augmented system. Experimental results show that the proposed method reduces the time for obtaining the non-zero structure of Cholesky factor L.
내부점기법에 있어서 효율적인 순서화와 자료구조 : 최소부족순서화를 중심으로 Putting Emphasis on the Minimum Deficiency Ordering
박순달,김병규,성명기 한국경영과학회 1996 韓國經營科學會誌 Vol.21 No.3
Ordering plays an important role in solving an LP problem with sparse matrix by the interior point method. Since ordering is NP-complete, we try to find an efficient heuristic method. The objective of this paper is to present an efficient heuristic ordering method for implementation of the minimum deficiency method. Both the ordering method and the data structure play important roles in implementation. First we define a new heuristic pseudo-deficiency ordering method and a data structure for the method - quotient graph and clique storage. Next we show an experimental result in terms of time and nonzero numbers by NETLIB problems.