We present a generalization to symmetric optimization of interior-point methods for linear optimization based on kernel functions. Symmetric optimization covers the three most common conic optimization problems: linear, second-order cone and semi-definite optimization problems. Namely, we adapt the interior-point algorithm described in Peng et al. [Self-regularity: A New Paradigm for Primal–Dual Interior-point Algorithms. Princeton University Press, Princeton, NJ, 2002.] for linear optimization to symmetric optimization. The analysis is performed through Euclidean Jordan algebraic tools and a complexity bound is derived.
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