Maryam Fazel, Haitham Hindi, and Stephen P. Boyd. A rank minimization heuristic with application to minimum order system approximation. In Proceedings American Control Conference, volume 6, 2001. Home/Search Document Not in Database Summary Related Articles Check |
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A Semidefinite Representation for some Minimum Cardinality.. - d'Aspremont (2003) (Correct)
....A related problem is that of minimizing the rank of a p.s.d. matrix subject to LMI constraints: subject to X (2) where is here an a#ne subset of the semidefinite cone (a LMI) In this case also, minimizing the nuclear norm #X# # of X will produce excellent approximate solutions (see [FHB00]) In this paper, using results by [Cas84] Sho87] Put93] CLR95] Nes00] Las01] PS01] and [Las02] we show that the MinCard(x) and MinRank(X) problems in (1) and (2) are equivalent to large semidefinite programs (see [NN94] To be precise, based on a reformulation a la [Sho87] of ....
....every instance of the problem, we are interested in finding an e#cient heuristic method for approximating the solution to all the problems to be solved. The complexity of the first bound design program will be high, but that of the subsequent programs will then be much lower. The heuristics in [FHB00] replaced the Card(x) resp. Rank(X) functions by their convex envelope on the sets 0 1 (resp. 0 I) i.e. the largest convex function f(x) such that f(x) Card(x) if 0 1 (resp. f(X) Rank(X) if 0 I) In this section, we extend these bounds to semialgebraic sets with more ....
M. Fazel, H. Hindi, and S. Boyd, A rank minimization heuristic with application to minimum order system approximation., Working paper. American Control Conference, September 2000 (2000).
Fast Linear Iterations for Distributed Averaging - Xiao, Boyd (2003) (2 citations) Self-citation (Boyd) (Correct)
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M. Fazel, H. Hindi, and S. Boyd. A rank minimization heuristic with application to minimum order system approximation. In Proc. American Control Conf., pages 4734--4739, Arlington, VA, June 2001.
Fast Linear Iterations for Distributed Averaging - Xiao, Boyd (2003) (2 citations) Self-citation (Boyd) (Correct)
....the convex problem minimize 1 Iwl (29) subject to r axI I A diag(w)n 11T n rnxI. It is also possible to assign weights to the edges, to achieve (hopefully) some desired sparsity pattern. More sophisticated heuristics for sparse design and minimum rank problems can be found in, e.g. [14]. 15 To demonstrate this idea, we applied the heuristic (29) to the example described in 5.1. We set the guaranteed convergence factor r TM z 0.910, which is only slightly larger than the minimum factor 0.902. The resulting edge weight vector is relatively sparse; the number of edges with ....
M. Fazel, H. Hindi, and S. Boyd. A rank minimization heuristic with application to minimum order system approximation. In Proceedings American Control Conference, volume 6, pages 4734 4739, Arlington, VA, June 2001.
Maximum-Margin Matrix Factorization - Srebro, Rennie, Jaakola (2005) (Correct)
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Maryam Fazel, Haitham Hindi, and Stephen P. Boyd. A rank minimization heuristic with application to minimum order system approximation. In Proceedings American Control Conference, volume 6, 2001.
Large-Margin Matrix Factorization - Srebro, Rennie, Jaakkola (2004) (Correct)
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Maryam Fazel, Haitham Hindi, and Stephen P. Boyd. A rank minimization heuristic with application to minimum order system approximation. In Proceedings American Control Conference, volume 6, 2001.
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