Abstract
The goal of this chapter is to establish the superlinear convergence of a path-following algorithm for semidefinite programming, without non-degeneracy assumptions. Specifically, we propose a predictor-corrector type algorithm with (r + 1)-step superlinear convergence of order 2/(1 + 2-r), where any positive integer can be assigned to the parameter r. The parameter r is used in the algorithm as an upper bound on the number of successive corrector steps that are allowed between two predictor steps. The proof of superlinear convergence is based on the properties of the central path that were derived in Chapter 5.
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© 2000 Springer Science+Business Media Dordrecht
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Frenk, H., Roos, K., Terlaky, T., Zhang, S. (2000). Superlinear Convergence. In: Frenk, H., Roos, K., Terlaky, T., Zhang, S. (eds) High Performance Optimization. Applied Optimization, vol 33. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3216-0_6
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DOI: https://doi.org/10.1007/978-1-4757-3216-0_6
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4819-9
Online ISBN: 978-1-4757-3216-0
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