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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?

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  • $\begingroup$ Why implement such a method yourself when there is great software already out there!? $\endgroup$
    – Wolfgang Bangerth
    Commented Oct 13, 2020 at 18:53
  • $\begingroup$ @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? $\endgroup$
    – Jogging Song
    Commented Oct 14, 2020 at 0:46
  • $\begingroup$ I have no experience with phone apps, sorry. $\endgroup$
    – Wolfgang Bangerth
    Commented Oct 14, 2020 at 1:13

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