Interior-point methods based on kernel functions for symmetric optimization

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.

Keywords:

• symmetric optimization
• interior-point methods
• kernel functions
• Jordan algebras

AMS Subject Classifications :

• 90C25
• 90C51

Acknowledgements

The author developed this work during his PhD studies at the Technical University of Delft, The Netherlands. The author kindly acknowledges his supervisor, Prof. dr. ir. C. Roos. The author also thanks anonymous referees for their comments that helped improve this paper. This work was partially supported by Financiamento Base 2009 ISFL-1-297 from FCT/MCTES/PT.