A polynomial primal-dual affine scaling algorithm for symmetric conic optimization

The primal-dual Dikin-type affine scaling method was originally proposed for linear optimization and then extended to semidefinite optimization. Here, the method is generalized to symmetric conic optimization using the notion of Euclidean Jordan algebras. The method starts with an interior feasible...

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Bibliographic Details
Published in:	Computational optimization and applications 2017-04, Vol.66 (3), p.577-600
Main Authors:	Mohammad-Nezhad, Ali, Terlaky, Tamás
Format:	Article
Language:	eng
Subjects:	Algorithms Conics Convex and Discrete Geometry Feasibility Management Science Mathematical models Mathematics Mathematics and Statistics Methods Operations Research Operations Research/Decision Theory Optimization Optimization algorithms Polynomials Scaling Statistics Studies Symmetry
Online Access:	Get full text
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Summary:	The primal-dual Dikin-type affine scaling method was originally proposed for linear optimization and then extended to semidefinite optimization. Here, the method is generalized to symmetric conic optimization using the notion of Euclidean Jordan algebras. The method starts with an interior feasible but not necessarily centered primal-dual solution, and it features both centering and reducing the duality gap simultaneously. The method’s iteration complexity bound is analogous to the semidefinite optimization case. Numerical experiments demonstrate that the method is viable and robust when compared to SeDuMi, MOSEK and SDPT3.
ISSN:	0926-6003 1573-2894