I need to slove one optimization problem of quadratic programming. The number of optimization variables is about 16,000. The constraints include equality constraints and inequality constraints.
I have no such practical experiences before. There are are three choices for the probelm after reading some materials:
active set method,
interior point method
augmented Lagrangian method
I need implement the optimization algorithm on my own.
Active set method is not suitable for such problem size.
Interior point method is fast but difficult to implement from the link:
https://scicomp.stackexchange.com/questions/14228/rank-deficient-nnls?noredirect=1&lq=1
A first order method (Augmented Lagrangian, ADMM, split Bregman, etc.) These are possible to implement yourself without needing to use a packaged library.
So augmented Lagrangian method will be my choice. How about my analysis?
Most materials I find is about augmented Lagrangian method with equality constraints. Can you recommand any links or materials on augmented Lagrangian method with inequality constraints?
@littleO has pointed you to the right references. And below is a simple trick for converting inequality constraints into equality constraints:
$$Ax \le b \quad \mbox{means} \quad Ax - b = t, \quad t \le 0.$$