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Chek Beng Chua(cbchuantu.edu.sg) Abstract: We extend the target map, together with the weighted barriers and the notions of weighted analytic centers, from linear programming to general convex conic programming. This extension is obtained from a novel geometrical perspective of the weighted barriers, that views a weighted barrier as a weighted sum of barriers for a strictly decreasing sequence of faces. Using the Euclidean Jordanalgebraic structure of symmetric cones, we give an algebraic characterization of a strictly decreasing sequence of its faces, and specialize this target map to produce a computationallytractable targetfollowing algorithm for symmetric cone programming. The analysis is made possible with the use of triangular automorphisms of the cone, a new tool in the study of symmetric cone programming. As an application of this algorithm, we demonstrate that starting from any given any pair of primaldual strictly feasible solutions, the primaldual central path of a symmetric cone program can be efficiently approximated. Keywords: Symmetric cone programming; targetfollowing algorithm; target map; weighted barrier; weighted analytic centers; flags of faces; triangular transformations. Category 1: Convex and Nonsmooth Optimization (Convex Optimization ) Category 2: Linear, Cone and Semidefinite Programming (Other ) Citation: Research Report, January 2011, Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore Download: [PDF] Entry Submitted: 01/03/2011 Modify/Update this entry  
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