Hi all,
I want to solve the heat equation T_t(x,t) = - L_x . T(x,t) + F(x,t) in an edge-weighted graph where L_x = \sum_i x_i e_{ij} is weighted Laplacian matrix of the graph. Then I conclude to the following least squares problem:
$$ \min_{x\in {0,1}} |\hat{T}_j(t_i) - T_j(t_i, x)|_2^2 $$

My question is that how I could formulate this expression in CVX despite that now there is not explicit variables in the norm term?

To use CVX, you must write your objective so that it is a convex function of the optimization variables (other than also possibly having integrality constraints), and indeed compliant with the DCP rules. Do you have such an explicit form? I’m thinking not. You may need a different optimization tool.

@Mark, I don’t have such a form. Because, I have done some experiments in continuous form. Now I need to compare the results with the discrete form. This is why I thought solving with cvx and branch and bound algorithm.

It sounds like you need a different tool. I don’t understand your problem well enough to know what that would be. Perhaps write out your problem in more detail and post on https://www.or-exchange.org/ .