TNPACK—A truncated Newton minimization package for large-scale problems: I. Algorithm and usage
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| Title: | TNPACK—A truncated Newton minimization package for large-scale problems: I. Algorithm and usage |
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| Authors: | Tamar Schlick, Aaron L. Fogelson |
| Source: | ACM Transactions on Mathematical Software. 18:46-70 |
| Publisher Information: | Association for Computing Machinery (ACM), 1992. |
| Publication Year: | 1992 |
| Subject Terms: | Software, source code, etc. for problems pertaining to operations research and mathematical programming, sparse matrices, Numerical computation of solutions to systems of equations, Numerical computation of matrix norms, conditioning, scaling, nonliner optimization, 0211 other engineering and technologies, 02 engineering and technology, Direct numerical methods for linear systems and matrix inversion, preconditioned conjugate gradient algorithm, Computational methods for sparse matrices, Numerical mathematical programming methods, Nonlinear programming, truncated Newton algorithm, FORTRAN package, Cholesky factorization |
| Description: | Summary: We present a FORTRAN package of subprograms for minimizing multivariate functions without constraints by a truncated Newton algorithm. The algorithm is especially suited for problems involving a large number of variables. Truncated Newton methods allow approximate, rather than exact, solutions to the Newton equations. Truncation is accomplished in the present version by using the preconditioned conjugate gradient algorithm (PCG) to solve approximately the Newton equations. The preconditioner \(M\) is factored in PCG using a sparse modified Cholesky factorization based on the Yale sparse matrix package. In this paper we briefly describe the method and provide details for program usage. |
| Document Type: | Article |
| File Description: | application/xml |
| Language: | English |
| ISSN: | 1557-7295 0098-3500 |
| DOI: | 10.1145/128745.150973 |
| Access URL: | https://nyuscholars.nyu.edu/en/publications/tnpack-a-truncated-newton-minimization-package-for-large-scale-pr-2 https://nyuscholars.nyu.edu/en/publications/tnpacka-truncated-newton-minimization-package-for-large-scale-pro-2 https://doi.acm.org/10.1145/128745.150973 https://dblp.uni-trier.de/db/journals/toms/toms18.html#SchlickF92 https://dl.acm.org/doi/10.1145/128745.150973 |
| Rights: | URL: https://www.acm.org/publications/policies/copyright_policy#Background |
| Accession Number: | edsair.doi.dedup.....73f31f1023a6ec6222ec87f7daa070d3 |
| Database: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstract: | Summary: We present a FORTRAN package of subprograms for minimizing multivariate functions without constraints by a truncated Newton algorithm. The algorithm is especially suited for problems involving a large number of variables. Truncated Newton methods allow approximate, rather than exact, solutions to the Newton equations. Truncation is accomplished in the present version by using the preconditioned conjugate gradient algorithm (PCG) to solve approximately the Newton equations. The preconditioner \(M\) is factored in PCG using a sparse modified Cholesky factorization based on the Yale sparse matrix package. In this paper we briefly describe the method and provide details for program usage. |
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| ISSN: | 15577295 00983500 |
| DOI: | 10.1145/128745.150973 |