Implementation method selection for sparse constrained linear least squares or quadratic programming

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:
rank-deficient NNLS
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?

• Why implement such a method yourself when there is great software already out there!? – Wolfgang Bangerth Oct 13 at 18:53
• @WolfgangBangerth The optimization solver need run on mobile phone. I hope to implement the solver myslef based on Eigen library. Do you have any suggestion? – Jogging Song Oct 14 at 0:46
• I have no experience with phone apps, sorry. – Wolfgang Bangerth Oct 14 at 1:13