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
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.
