Please use this identifier to cite or link to this item: 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
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