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A Mizuno-Todd-Ye predictor-corrector infeasible-interior-point method for linear programming over symmetric cones. (English) Zbl 1346.90580
Summary: 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.

MSC:
90C05 Linear programming
90C25 Convex programming
90C51 Interior-point methods
Software:
SDPLIB
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