Some Jordan algebras were proved more than a decade ago to be an indispensable tool in the unified study of interior-point methods. By using it, we generalize the infeasible interior-point method for linear optimization of Roos [SIAM J. Optim., 16(4):1110--1136 (electronic), 2006] to symmetric optimization. This unifies the analysis for linear, second-order cone and semidefinite optimizations.
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