CVX long formulation time for large scale least square

[Mark_L_Stone]

There are two stages to getting the solution: Model formulation by CVX and model solving by the solver. Perhaps a lot of the time is due to CVX model formulation (during which there will be no output on the screen).

Vectorization should help tremendously with model formulation time.

How to vectorize most constraint loops in CVX

Using permute and repmat, most constraint loops in CVX can be eliminated. For example, the following: variables X(N) Y(M) Z(N); for n=1:N for m=1:M if n~=m && n^3>m^2 X(n)>=Y(m)+Z(n); % (1) end end end The first step is to expand. (1) actually means there are M*N constraints, so X is expanded to repmat(X,1,M), Y is expanded to repmat(Y,1,N), Z(n) is expanded to repmat(Z,1,M), according to their original dimensions. Now, repmat(X,1,M) is a N-by-M matrix, rep…