The MOSEK command line tool Version 7.0 (Revision 141)

5.6. SOLVING PROBLEMS IN PARALLEL 47
5.6.2 The parallelized interior-point optimizer
The interior-point optimizer is capable of using multiple CPUs or cores. This implies that whenever
the MOSEK interior-point optimizer solves an optimization problem, it will try to divide the work so
that each core gets a share of the work. The user decides how many coress MOSEK should exploit.
It is not always possible to divide the work equally, and often parts of the computations and the
coordination of the work is processed sequentially, even if several cores are present. Therefore, the
speed-up obtained when using multiple cores is highly problem dependent. However, as a rule of
thumb, if the problem solves very quickly, i.e. in less than 60 seconds, it is not advantageous to use
the parallel option.
The MSK IPAR NUM THREADS parameter sets the number of threads (and therefore the number of cores)
that the interior point optimizer will use.
5.6.3 The concurrent optimizer
An alternative to the parallel interior-point optimizer is the concurrent optimizer. The idea of the
concurrent optimizer is to run multiple optimizers on the same problem concurrently, for instance,
it allows you to apply the interior-point and the dual simplex optimizers to a linear optimization
problem concurrently. The concurrent optimizer terminates when the first of the applied optimizers
has terminated successfully, and it reports the solution of the fastest optimizer. In that way a new
optimizer has been created which essentially performs as the fastest of the interior-point and the
dual simplex optimizers. Hence, the concurrent optimizer is the best one to use if there are multiple
optimizers available in MOSEK for the problem and you cannot say beforehand which one will be
faster.
Note in particular that any solution present in the task will also be used for hot-starting the simplex
algorithms. One possible scenario would therefore be running a hot-start dual simplex in parallel with
interior point, taking advantage of both the stability of the interior-point method and the ability of
the simplex method to use an initial solution.
By setting the
MSK IPAR OPTIMIZER
parameter to
MSK OPTIMIZER CONCURRENT
the concurrent optimizer chosen.
The number of optimizers used in parallel is determined by the
MSK IPAR CONCURRENT NUM OPTIMIZERS.
parameter. Moreover, the optimizers are selected according to a preassigned priority with optimizers
having the highest priority being selected first. The default priority for each optimizer is shown in
Table 5.6.3. For example, setting the MSK IPAR CONCURRENT NUM OPTIMIZERS parameter to 2 tells the
concurrent optimizer to the apply the two optimizers with highest priorities: In the default case that
means the interior-point optimizer and one of the simplex optimizers.