# CVX optimisation prroblem

I am unable to code the following optimisation problem in cvx.

Here, W is an nxn weight matrix and x is an nx1 vector. I want to find a weight matrix W that minimises the following objective function.

\begin{array}{r}{\varepsilon(W)=\sum_{i=1}^{n}\left\|x_{i}-\sum_{j \ne i} W_{(i, j)} x_{j}\right\|} \\ {\text { s.t. } \sum_{j} W_{(i, j)}=1}\end{array}
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Have you read the CVX Usersâ€™ Guide http://cvxr.com/cvx/doc/? This problem is quite straightforward to enter in CVX. After you have read the CVX Usersâ€™ Guide, if you are still stuck on something, please describe where you need help.

Yes I read the documentation for a long time but still couldnâ€™t identify a case similar to mine where Iâ€™m iterating over the elements of a vector and elements of matrix and has sum of norms in it.

I am not that familiar with high level optimisation theory as well.

It would be great help if you direct me to a similar example in the documentation, or provide me some hints to represent my objective function as a product of matrices and then I could maybe use sum and norms functions.

Each argument of the norm is a scalar, so the norm (regardless of â€śpâ€™â€ť) just amounts to absolute value of its argument. You can compute the objective in this case the same as you would if W were a numerical matrix in MATLAB.

You are allowed in CVX to do the following:

Objective = 0
for i=1:n
Objective = Objective + cvx_expression_this_time_through_for_loop
end
minimize(Objective)


Vectorization (avoiding for loops) is faster in CVX model processing time when you can do it, but for loops are always valid.