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: | Wang G, Bai Y |
Keywords: | programming: linear, heuristics |
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.