A primal--dual symmetric relaxation for homogeneous conic systems
Journal of Complexity
A descent method for a reformulation of the second-order cone complementarity problem
Journal of Computational and Applied Mathematics
Computational Optimization and Applications
Smoothing algorithms for complementarity problems over symmetric cones
Computational Optimization and Applications
The solution set structure of monotone linear complementarity problems over second-order cone
Operations Research Letters
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We present a general framework whereby analysis of interior-point algorithms for semidefinite programming can be extended verbatim to optimization problems over all classes of symmetric cones derivable from associative algebras. In particular, such analyses are extendible to the cone of positive semidefinite Hermitian matrices with complex and quaternion entries, and to the Lorentz cone. We prove the case of the Lorentz cone by using the embedding of its associated Jordan algebra in the Clifford algebra. As an example of such extensions we take Monterio's polynomial-time complexity analysis of the family of similarly scaled directions--introduced by Monteiro and Zhang (1998)--and generalize it to cone-LP over all representable symmetric cones.