On Commutative Class of Search Directions for Linear Programming over Symmetric Cones
نویسنده
چکیده
The Commutative Class of search directions for semidefinite programming is first proposed by Monteiro and Zhang [13]. In this paper, we investigate the corresponding class of search directions for linear programming over symmetric cones, which is a class of convex optimization problems including linear programming, second-order cone programming, and semidefinite programming as special cases. Complexity results are established for short, semi-long, and long step algorithms. We then propose a subclass of Commutative Class of search directions which has polynomial complexity even in semi-long and long step settings. The last subclass still contains the NT and HRVW/KSH/M directions. An explicit formula to calculate any member of the class is also given.
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