MATLAB: Solving Optimisation Problem with Rank Constraint in MATLAB

matricesmatrix manipulationoptimizationrank 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 180×16 matrix(C is rank deficient,i.e rank(C)=7), x is 4×4 matrix & d is 180×1 vector. However, I have a constraint that rank(x)=1. If x was a 16×1 vector and didn't have rank constraint, this problem could be easily solved by using y = pinv(C)*d in MATLAB. But since x is a matrix and has rank constraint, I am not able to proceed further. I would be grateful if someone provides me hint or suggestion to tackle this problem.

Best Answer

1. Solve y=pinv(C)*d
2. Determine the best rank-1 - approximation x to y as discussed in the previous thread:
http://www.mathworks.com/matlabcentral/answers/255420-representing-a-matrix-as-a-product-of-two-matrices-in-matlab
My guess is that x solves your original problem, but I'm not 100% certain.
Best wishes
Torsten.
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