Hi

How can i solve joint norm using CVX, for solving these form of problem;

min ||X||_2,1 s.t. ||Y-HX|| < err or min ||Y-HX||_2^2 + lambda*||AX||_2,1

Regards

Hi

How can i solve joint norm using CVX, for solving these form of problem;

min ||X||_2,1 s.t. ||Y-HX|| < err or min ||Y-HX||_2^2 + lambda*||AX||_2,1

Regards

What exactly is the 2,1 norm?

Is your 2,1 norm

`norms(norms(X,2,2),1,1)`

or perhaps

`norms(norms(P,1,2),2,1)`

help norms

norms Computation of multiple vector norms.

norms( X ) provides a means to compute the norms of multiple vectors

packed into a matrix or N-D array. This is useful for performing

max-of-norms or sum-of-norms calculations.`All of the vector norms, including the false "-inf" norm, supported by NORM() have been implemented in the norms() command. norms(X,P) = sum(abs(X).^P).^(1/P) norms(X) = norms(X,2). norms(X,inf) = max(abs(X)). norms(X,-inf) = min(abs(X)). If X is a vector, these computations are completely identical to their NORM equivalents. If X is a matrix, a row vector is returned of the norms of each column of X. If X is an N-D matrix, the norms are computed along the first non-singleton dimension. norms( X, [], DIM ) or norms( X, 2, DIM ) computes Euclidean norms along the dimension DIM. norms( X, P, DIM ) computes its norms along the dimension DIM. Disciplined convex programming information: norms is convex, except when P<1, so an error will result if these non-convex "norms" are used within CVX expressions. norms is nonmonotonic, so its input must be affine.`

It looks like your example in effect reshapes a vector into a matrix, then computes the 2-norms across the rows, then sums those results.

So here is a guess, which you should check (input numerical values for X, and make sure the calculation is correct).

`sum(norms(reshape(X,M,N),2,2))`

If this isnâ€™t correct, it should be something similar, which you should be able to figure out.