In this paper,we present two primal�??dual interior-point algorithms for symmetric
cone optimization problems. The algorithms produce a sequence of iterates in
the wide neighborhood N(�?, β) of the central path. The convergence is shown for a
commutative class of search directions, which includes the Nesterov�??Todd direction
and the xs and sx directions.We derive that these two path-following algorithms have
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O\br |
√
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r\cond(G)
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logε−1,O\br√r\br\cond(G)1/4logε−1 |
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iteration complexity bounds, respectively. The obtained complexity bounds are the best
result in regard to the iteration complexity bound in the context of the path-following
methods for symmetric cone optimization. Numerical results show that the algorithms
are efficient for this kind of problems.
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