Given the system of equations
$Ax=b$, subject to $Cx\le d$
where $A$ is an $n\times m$ matrix (with $n>m$) and is very large and sparse. As an example $A$ can have $3126250\times 2740$ elements. Each row of $A$ has only 4 or 5 non-zero numbers which can only be 1 or -1.
I am on Matlab and I've been using LSQR but I need the inequality constraints to impose monotonicity on $x$.
Can you please advise on any solvers to do this with linear constraints? Is there any implementation on Matlab or C for this?