Thursday, January 30, 2025

MOSEK 11 is now available

 MOSEK 11 has now been released!

You will find all the necessary information, installation instructions and documentation on the website of the new version. To try it out you must obtain a new license file, either by applying/reapplying for a trial/academic license on our website or contacting our sales if a customer.

The main features of MOSEK 11 are

  • substantial efficiency improvements in the mixed-integer optimizer,
  • a new API for MATLAB,
Enjoy MOSEK 11 and we are looking forward to your feedback.

The MOSEK team

Thursday, January 16, 2025

The interior-point optimizer and warm-start

A frequently asked question by MOSEK users is whether the interior-point optimizer can be warm-started. The short answer is that no warm-start is available for the interior-point optimizer.

The reason for the lack of a warm-start capability is that no general-purpose interior-point warm-starting method that

  • is robust i.e. numerical stable,
  • and leads to consistent performance benefits
has been suggested,

The paper contains some limited computational evidence that an interior-point warm-start may be possible.  Note that the paper shows that in the best case where both a good primal and dual solution guesses are available, the number of iterations is reduced by 50%.  However, the paper does not consider the complications of integrating the warm-start with the presolve procedure in a commercial optimizer like MOSEK. Also, an interior-point method benefits a lot from the presolve and which has a fairly computationally expensive setup step that is independent of a warm-start.  Hence, a large reduction in the number of iterations does not translate into an equally large decrease in the optimizer time due to a large initialization cost.

Based on the discussion above it can be concluded that how to warm-start an interior-point optimizer is an open question. Furthermore, obtaining a 50% reduction in the optimizer time by wam-starting is unlikely even if it was possible to warm-start. Something like from 0 to 25% reduction in the optimizer time is much more likely if a good warm-start method was known.