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An arc-search infeasible-interior-point method for symmetric optimization in a wide neighborhood of the central path. (English) Zbl 06737238
Summary: In this paper, we propose a new arc-search infeasible-interior-point method for symmetric optimization using a wide neighborhood of the central path. The proposed algorithm searches for optimizers along the ellipses that approximate 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. The complexity bound is \(\mathcal {O}(r^{5/4}\log \varepsilon ^{-1})\) for the Nesterov-Todd direction, and \(\mathcal {O}(r^{7/4}\log \varepsilon ^{-1})\) for the \(xs\) and \(sx\) directions, where \(r\) is the rank of the associated Euclidean Jordan algebra and \(\varepsilon \) is the required precision. The obtained complexity bounds coincide with the currently best known theoretical complexity bounds for the short step path-following algorithm. Some limited encouraging computational results are reported.

90C Mathematical programming
Netlib; SDPLIB
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