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|Title:||A note on the calculation of step-lengths in interior-point methods for semidefinite programming|
|Keywords:||Interior point methods|
|Source:||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|
|Appears in Collections:||Staff Publications|
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