- A primal-dual symmetric relaxation for homogeneous conic systems Juan Vera (jveraandrew.cmu.edu) Juan Rivera (juanrandrew.cmu.edu) Javier Pena (jfpandrew.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 n-dimensional Euclidean space. We reformulate this pair of conic systems as a primal-dual 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 self-scaled cone with a known self-scaled barrier, the conic programming reformulation can be solved via interior-point methods. For a well-posed instance A, a strict solution to one of the two original conic systems can be obtained in a number of interior-point iterations proporcional to Renegar's condition number of the matrix A, namely, the reciprocal of the relative distance from A to the set of ill-posed instances. Keywords: conic systems, primal-dual methods, interior-point methods Category 1: Convex and Nonsmooth Optimization (Convex Optimization ) Citation: Download: [Postscript][PDF]Entry Submitted: 04/27/2002Entry Accepted: 04/29/2002Entry Last Modified: 04/27/2002Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.