# Could L21 norm be built in objective function?

Hello Everyone!
At present I am working with a project using Sparse Subspace coding technique. And I’m new to CVX.
it is only the l21 norm which locates in the g() function i cannot write into the objective function. The l21 norm is defined as this .

Could it be solved by cvx? Or other toolbox recommendations?

Presuming the sum is over all columns in C,
`sum(norms(C))`
should be what you want.

`````` 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.``````
2 Likes

Thanks a lot.
The example file uses a vector as variable. And from here I was taught that matrix could be variable and even as a parameter to a function used in the cvx sentence. Thank you for your help!