Interior-point methods based on kernel functions for symmetric optimization

Citation:
Vieira, Manuel V. C. "Interior-point methods based on kernel functions for symmetric optimization." Optimization Methods and Software. 27.3 (2012): 513-537.

Abstract:

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.

Notes:

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