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:
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?