Abstract
We propose a Mizuno–Todd–Ye predictor-corrector infeasible-interior-point method for linear programming over symmetric cones by using a wide neighborhood. In the corrector step, we adopt a special strategy, which can ensure the existence of a step size to keep every iteration in the given small neighborhood. By using an elegant analysis, we obtain the iteration bounds for a commutative class of directions. In particular, the iteration bound is \(\mathcal {O}(r\log \varepsilon ^{-1})\) for the Nesterov-Todd search direction, and \(\mathcal {O}(r^{3/2}\log \varepsilon ^{-1})\) for the xs and sx search direction. To our knowledge, the obtained iteration bounds match the currently best known iteration bounds for infeasible-interior-point method. Some preliminary numerical results are provided as well.
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Yang, X., Zhang, Y., Liu, H. et al. A Mizuno-Todd-Ye predictor-corrector infeasible-interior-point method for linear programming over symmetric cones. Numer Algor 72, 915–936 (2016). https://doi.org/10.1007/s11075-015-0074-7
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DOI: https://doi.org/10.1007/s11075-015-0074-7