The quadratic programming objective function for MATLAB and Octave is:
$$J_{min} = \frac{1}{2}x^THx + x^Tq$$
and the constraints are:
$$lb <= x <= ub$$ $$Ax = b$$
In this case, I want to use the qp-command from Octave because I don't have MATLAB on my computer. The qp-command differes from MATLAB's quadprog command, but the results are the same.
The command qp:
[x, obj, info, lambda] = qp (x0, H, q, A, b, lb, ub)
Octave - 25.2 Quadratic Programming
Question:
I only want lower bounds and upper bounds constraints on vector $x$. The command need to have a value of vector $b$ and matrix $A$, which I don't have in my case. Can I say that the command should then be:
[x, obj, info, lambda] = qp (x0, H, q, I, Ix, lb, ub)
if I want to avoid setting any equality constraints? I want to set value of $b = Ix$ and just set $A = I$ to the identity matrix, and only focus on lower bound limit and upper bound limit.
What do I need to set $x_0$ to? The past $x$?
Does this work?
If you don't have equality constraints, you set them to [] to indicate this.
$x_0$ is your best guess, but it has to be a feasible guess. Most often it doesn't help much to warm-start with a guess unless it is very close to the optimal one, so you simply set it to [] and the solver will cold-start.