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- r = 2; % the rank;
- N = 32; % the dimension
- M = 32;
- a = randn(N,r);
- b = randn(M,r);
- X = a*b'; % low rank Matrix;
- A = rand(20,N);
- Y = A*X;
- % low rank approximation using nuclear norm
- cvx_begin
- variable Xe(N,M)
- minimize norm_nuc(Xe);
- subject to A*Xe == Y;
- cvx_end
- number of iterations = 8 primal objective value = 5.75866738e+01 dual objective value = 5.75866738e+01 gap := trace(XZ) = 3.73e-08 relative gap = 3.21e-10 actual relative gap = 3.49e-10 rel. primal infeas (scaled problem) = 6.90e-11 rel. dual " " " = 1.50e-12 rel. primal infeas (unscaled problem) = 0.00e+00 rel. dual " " " = 0.00e+00 norm(X), norm(y), norm(Z) = 8.4e+01, 1.6e+00, 4.2e+00 norm(A), norm(b), norm(C) = 6.0e+01, 1.6e+02, 5.1e+00 Total CPU time (secs) = 1.75 CPU time per iteration = 0.22 termination code = 0
- DIMACS: 4.9e-10 0.0e+00 3.8e-12 0.0e+00 3.5e-10 3.2e-10 Status: Solved
- Optimal value (cvx_optval): +57.5867
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