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 November 19th, 2015, 02:43 AM #1 Newbie   Joined: Nov 2015 From: Germany Posts: 2 Thanks: 0 Optimisation Problem with Rank Constraint I have a typical least squares problem, i.e I have to find the value of x that minimizes norm of C∗x−d. C is 180x16 matrix, x is 16x1 vector & d is 180x1 vector. However, matrix C is rank deficient (rank(C)=7. Also, I want to represent 16x1 vector x by a 4x4 matrix of rank 1. I have solved it by using normal equation and SVD but the 4x4 matrix that I have obtained from x has rank 4. Is there some constraint that I need to add in my problem in order to get this 4x4matrix of rank 1 from vector x? I would appreciate any suggestion/hint on this type of optimisation problem. November 19th, 2015, 08:42 AM #2 Banned Camp   Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126 Linear combinations of the columns of the 4X4 matrix M won't change the rank. However, it might be possible to find ai to create a matrix polynomial from M of rank 1: P(M)=a0I+a1M+a2M^2+.. The key question is, how do you find the rank of a matrix polynomial. Nothing on Google. Tags constraint, convex optimization, leastsquares, optimisation, problem, rank Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post sm2n10 Calculus 0 June 6th, 2015 11:53 PM sk3blue Calculus 2 February 15th, 2015 11:51 PM Doc Calculus 4 September 12th, 2013 02:02 AM helloprajna Economics 0 February 17th, 2013 11:04 PM Justin Lo Applied Math 0 December 8th, 2009 02:40 AM

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