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Correlative sparsity in primal-dual interior-point methods for LP, SDP, and SOCP

Title
Correlative sparsity in primal-dual interior-point methods for LP, SDP, and SOCP
Authors
Kobayashi K.Kim S.Kojima M.
Ewha Authors
김선영
SCOPUS Author ID
김선영scopus
Issue Date
2008
Journal Title
Applied Mathematics and Optimization
ISSN
0095-4616JCR Link
Citation
vol. 58, no. 1, pp. 69 - 88
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
Exploiting sparsity has been a key issue in solving large-scale optimization problems. The most time-consuming part of primal-dual interior-point methods for linear programs, second-order cone programs, and semidefinite programs is solving the Schur complement equation at each iteration, usually by the Cholesky factorization. The computational efficiency is greatly affected by the sparsity of the coefficient matrix of the equation which is determined by the sparsity of an optimization problem (linear program, semidefinite program or second-order cone program). We show if an optimization problem is correlatively sparse, then the coefficient matrix of the Schur complement equation inherits the sparsity, and a sparse Cholesky factorization applied to the matrix results in no fill-in. © 2007 Springer Science+Business Media, LLC.
DOI
10.1007/s00245-007-9030-9
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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