Abstract
We present a new infeasible-interior-point method, based on a wide neighborhood, for symmetric cone programming. The convergence is shown for a commutative class of search directions, which includes the Nesterov–Todd direction and the xs and sx directions. Moreover, we derive the complexity bound of the wide neighborhood infeasible interior-point methods that coincides with the currently best known theoretical complexity bounds for the short step path-following algorithm.
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Acknowledgements
We are grateful to the anonymous referees and editor for their useful comments that help us improve the presentation of this paper. We would also like to thank the supports of National Natural Science Foundation of China (NNSFC) under Grant Nos. 61072144 and 61179040.
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Communicated by Florian A. Potra.
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Liu, H., Yang, X. & Liu, C. A New Wide Neighborhood Primal–Dual Infeasible-Interior-Point Method for Symmetric Cone Programming. J Optim Theory Appl 158, 796–815 (2013). https://doi.org/10.1007/s10957-013-0303-y
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DOI: https://doi.org/10.1007/s10957-013-0303-y