Manually fixing initial point in an SDP

[Nathaniel Joseph Morrison]

Dear all,

I hope you are well! We've come across a situation in which it would be potentially very useful to be able to manually set the initial guess for the solution matrix X in an SDP.

In brief, we are solving a sequence of SDPs with identical constraints, but slightly different objectives. We have confirmed that the elements of X in the solution to succeeding problems differ by on average 5%, so it would seem that using the results of the previous SDP as the intial guess for the next SDP might significantly reduce computation time.

I know LPs can use a "hot start", and there is an iparam.intpnt_hotstart parameter (though its description simply says "currently not in use"); is there any way to either control initialization or use a hot start for SDPs?

All the best,

Nathaniel Morrison

[Erling D. Andersen]

Hi

The interior-point optimizer cannot be hotstarted. Only the simplex optimizers can.

I am currently experimenting with hotstarting it in the linear case. If I can get that working well, we might try out the nonlinear case too.

Whether this will ever be of sufficiently good quality which can be released is hard to say. 

[Nathaniel Joseph Morrison]

Hello!

Thanks for the information! I take it user-defined initialization is also not possible then?

Best,

Nathaniel

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[Erling D. Andersen]

Hi

Since we got that question several times then here is bit more explicit reply.

Yes, there is no way to specify the starting point that the interior-point optimizer starts from.

Btw at least I do not know how to do hotstart efficiently an interior-point algorithm in the linear case which is simpler than SDP case.

So it is an open question both in theory and practice to do what you want.   

Without getting into details then reducing the time by say 50% using hotstart would be a spectacular result. This nowhere near the benefit you often get from simplex hotstart.