0

I have a series of conic programming problems to solve. After solving the first one, I get one correct result. However, as the second optimization problem is really similar to the former one, I want to take advantage of the first solution to accelerate the process. After reading the documentation of mosek on Matlab, it seems that it is hard to use a warm start for conic optimization problem in mosek? I wonder if there is some way to handle this because it is really disappointing to solve a series of conic optimization problems from scratch every time. Thank you in advance!

Mengxiao Zhang
  • 31
  • 3

1 Answers1

0

I'm pretty sure, that all conic-problems are solved by the/one of the IPM-methods in Mosek.

IPMs are known for a somewhat problematic warm-start theory (and some papers on the topic from a few years ago still said: no gain compared to re-solving).

In your case, there is probably only one thing to take from the docs here:

Currently, the interior-point optimizer in MOSEKcannot take advantage of a previous optimal solution, however, the simplex optimizer can exploit any basic solution.

(We don't know your problem and needs, but the open-source solver SCS, which also has many wrappers, can use warm-starts. It's not an IPM-method (ADMM), might be faster in general (and can use GPU), but also might be less accurate).

sascha
  • 32,238
  • 6
  • 68
  • 110
  • Thank you very much. The problem is just to get the solution of a sequence of SDP problems, and I also find the SCS framework which allows a warm start. However, the documentation of SCS seems confusing and it seems that for semidefinite programming, we can only use CVX in SCS, which is really slow when solving large systems. – Mengxiao Zhang Aug 17 '17 at 14:56
  • CVX is a modelling tool (which proves convexity by construction which has some overhead). You can use SCS without it, if you are able to formulate it in standard-form. – sascha Aug 17 '17 at 15:04