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Abstract: . In this paper, we give an example of a semidefinite programming problem in which primal-dual affine-scaling algorithms using the HRVW/KSH/M, MT, and AHO directions fail. We prove that each of these algorithm can generate a sequence converging to a non-optimal solution, and that, for the AHO direction, even its associated continuous trajectory can converge to a non-optimal point. In contrast with these directions, we show that the primal-dual affine-scaling algorithm using the NT direction for ... (Update)
Context of citations to this paper: More
...s affine scaling algorithm could be very fast. However this algorithm may not even converge. Muramatsu [22] and Muramatsu and Vanderbei [23] showed an example in which these affine scaling algorithms will not converge to an optimal answer. There are also quite a few...
...in [26] can be used for other non path following schemes as well. For primal dual affine scaling method, Muramatsu and Vanderbei [20] investigated the performance of various search directions. For several of the known search directions they showed that the convergence fails,...
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BibTeX entry: (Update)
M. Muramatsu and R. Vanderbei, "Primal-dual affine scaling algorithms fail for semidefinite programming, " Technical Report, SOR, Princeton University, Princeton, NJ, 1997. http://citeseer.ist.psu.edu/article/muramatsu98primaldual.html More
@article{ muramatsu99primaldual,
author = "M. Muramatsu and R. J. Vanderbei",
title = "Primal-dual affine-scaling algorithms fail for semidefinite programming",
journal = "Mathematics of Operations Research",
volume = "24(1)",
pages = "149--175",
year = "1999",
url = "citeseer.ist.psu.edu/article/muramatsu98primaldual.html" }
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