I have a question about solving large sparse matrix LP problem. It really confused me for a long time.
If I have a form like this:
I have all Fi data, which are in sparse form. How can I build a LP model to solve this problem faster? Any clue? Thank you!

Second, please read PSA: make it easier to help you. Itâ€™s a lot easier to help if you can share a minimum working example showing what you have already tried.

Thank you, odow! Actually, I use Julia JuMP. I am confused about how to realize the constraint ciâ€™Xci>=0. X here is a large sparse matrix. The dimension of X is 1512*1512.

Q=sparse(eigvecs(Y)) //Y is value of variable X
for i=1:1512
if P[i]<=-1.0e-5 // P[i] is the ith eigenvalue of X
@constraint(model, Q[:,i]'*X*Q[:,i]>=0) //(Q[:,i] is the ith eigenvector of X)
end
end

When I run this code, I got this â€śWarning: The addition operator has been used on JuMP expressions a large number of times. This warning is safe to ignore but may indicate that model generation is slower than necessary. For performance reasons, you should not add expressions in a loop. Instead of x += , use append!(x,y) to modify x in place. Uf y is a single variable, you may also use push!(x, coef, y) in place of x += coef*yâ€ť.