Abstract
Two primal-dual affine scaling algorithms for linear programming are extended to semidefinite programming. The algorithms do not require (nearly) centered starting solutions, and can be initiated with any primal-dual feasible solution. The first algorithm is the Dikin-type affine scaling method of Jansen et al. (1993b) and the second the classical affine scaling method of Monteiro et al. (1990). The extension of the former has a worst-case complexity bound of O(τ0nL) iterations, where τ0 is a measure of centrality of the the starting solution, and the latter a bound of O(τ0nL2) iterations.
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de Klerk, E., Roos, C. & Terlaky, T. Polynomial Primal-Dual Affine Scaling Algorithms in Semidefinite Programming. Journal of Combinatorial Optimization 2, 51–69 (1998). https://doi.org/10.1023/A:1009791827917
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DOI: https://doi.org/10.1023/A:1009791827917