disciplined optimization with matrix variable

[Cecco Angiolieri]

Hi,

I am having a hard time in setting up in cxvopt a problem I can easily write. The main problem is that the variable is a 2D array, say X with dimension NxN. Here it is (let "1" be the array of all 1s)

max_X    norm(X)

       s.t.   X' * 1 < m (sum of each column less than a given constant, X' is the transpose and m a given constant real array)

               0 < X < G (element-wise, G is a given constant real matrix)

               X_i * 1 > X_{i+1} *1 (sum of each row greater than next row, i=0,...,N-1)

What should I do to obtain a formulation consistent with cxvopt definitions?

P.S. I tried with some of the high level parsers (picos, specifically), but it turned out to be very slow in parsing the constraints (my N is >2.5k), so I wanted to give it a try in "native" cvxopt.

Thank you!