[Cbc] Linear System Constraint Least Square

[soufiane khiat]

Hello,

I'm new on Optimization topic. I try to minimize:
||Ax-b||_2
Subject to a list of constraint {B_i, L_ij, E_ij}:
B_i (each x_i could have a: no bound, min bound, max bound or both):
min_i<=x_i<=max_i

L_ij (with i != j, (i,j) On [1..N]):
x_i + x_j = u_ij With u_ij = {0 OR 1}

E_ij (with i != j, (i,j) On [1..N]):
u_i >= x_i
u_j >= x_j
u_i + u_j <= 1 With (u_i, u_j) is Binary variable like u_ij on L_ij.

I have no control on size of data, number of B_i, L_ij and E_ij it is only
a data.
A is a Matrix NxM, x and b is a vector. So I would like to find best as
possible x to satisfact this constraints.

My question is, how can I fill a CbcModel to describ this problem without
*.mps file?
It is possible to only provide a Matrix A and b?

Thanks for you answers.

Soufiane KHIAT
Software Engineer
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