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https://doi.org/10.1023/A:1013777203597
Title: | A note on the calculation of step-lengths in interior-point methods for semidefinite programming | Authors: | Toh, K.-C. | Keywords: | Interior point methods Lanczos iteration Semidefinite programming Step-length |
Issue Date: | Mar-2002 | Citation: | Toh, K.-C. (2002-03). A note on the calculation of step-lengths in interior-point methods for semidefinite programming. Computational Optimization and Applications 21 (3) : 301-310. ScholarBank@NUS Repository. https://doi.org/10.1023/A:1013777203597 | Abstract: | In each iteration of an interior-point method for semidefinite programming, the maximum step-length that can be taken by the iterate while maintaining the positive semidefiniteness constraint needs to be estimated. In this note, we show how the maximum step-length can be estimated via the Lanczos iteration, a standard iterative method for estimating the extremal eigenvalues of a matrix. We also give a posteriori error bounds for the estimate. Numerical results on the performance of the proposed method against two commonly used methods for calculating step-lengths (backtracking via Cholesky factorizations and exact eigenvalues computations) are included. | Source Title: | Computational Optimization and Applications | URI: | http://scholarbank.nus.edu.sg/handle/10635/102713 | ISSN: | 09266003 | DOI: | 10.1023/A:1013777203597 |
Appears in Collections: | Staff Publications |
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