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T-algebras and linear optimization over symmetric cones

Chek Beng Chua(cbchua***at***ntu.edu.sg)

Abstract: Euclidean Jordan-algebra is a commonly used tool in designing interior point algorithms for symmetric cone programs. T-algebra, on the other hand, has rarely been used in symmetric cone programming. In this paper, we use both algebraic characterizations of symmetric cones to extend the target-following framework of linear programming to symmetric cone programming. Within this framework, we design an efficient algorithm that finds the analytic centers of convex sets described by linear matrix and convex quadratic constraints.

Keywords: Symmetric cone programming; T-algebra; Target-following algorithm

Category 1: Linear, Cone and Semidefinite Programming (Other )

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: Pre-print, School of Physical & Mathematical Sciences, Nanyang Technological University, Singapore, June 2008

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Entry Submitted: 06/22/2008
Entry Accepted: 06/23/2008
Entry Last Modified: 06/22/2008

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