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Juan Vera (jveraandrew.cmu.edu) Abstract: We address the feasibility of the pair of alternative conic systems of constraints Ax = 0, x \in C, and A^T y \in C^*, defined by an m by n matrix A and a cone C in the ndimensional Euclidean space. We reformulate this pair of conic systems as a primaldual pair of conic programs. Each of the conic programs corresponds to a natural relaxation of each of the two conic systems. When C is a selfscaled cone with a known selfscaled barrier, the conic programming reformulation can be solved via interiorpoint methods. For a wellposed instance A, a strict solution to one of the two original conic systems can be obtained in a number of interiorpoint iterations proporcional to Renegar's condition number of the matrix A, namely, the reciprocal of the relative distance from A to the set of illposed instances. Keywords: conic systems, primaldual methods, interiorpoint methods Category 1: Convex and Nonsmooth Optimization (Convex Optimization ) Citation: Download: [Postscript][PDF] Entry Submitted: 04/27/2002 Modify/Update this entry  
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