A New Full Nesterov–Todd Step Primal–Dual Path‐Following Interior‐Point Algorithm for Symmetric Optimization

A New Full Nesterov–Todd Step Primal–Dual Path‐Following Interior‐Point Algorithm for Symmetric Optimization

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Article ID: iaor20124799
Volume: 154
Issue: 3
Start Page Number: 966
End Page Number: 985
Publication Date: Sep 2012
Journal: Journal of Optimization Theory and Applications
Authors: ,
Keywords: programming: linear, heuristics
Abstract:

In this paper, we generalize a primal–dual path‐following interior‐point algorithm for linear optimization to symmetric optimization by using Euclidean Jordan algebras. The proposed algorithm is based on a new technique for finding the search directions and the strategy of the central path. At each iteration, we use only full Nesterov–Todd steps. Moreover, we derive the currently best known iteration bound for the small‐update method. This unifies the analysis for linear, second‐order cone, and semidefinite optimizations.

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