The MOSEK command line tool Version 7.0 (Revision 141)

36 CHAPTER 5. THE OPTIMIZERS FOR CONTINUOUS PROBLEMS
5.1.3 Scaling
Problems containing data with large and/or small coefficients, say 1.0e + 9 or 1.0e − 7 , are often hard
to solve. Significant digits may be truncated in calculations with finite precision, which can result in
the optimizer relying on inaccurate calculations. Since computers work in finite precision, extreme
coefficients should be avoided. In general, data around the same ”order of magnitude” is preferred,
and we will refer to a problem, satisfying this loose property, as being well-scaled. If the problem is
not well scaled, MOSEK will try to scale (multiply) constraints and variables by suitable constants.
MOSEK solves the scaled problem to improve the numerical properties.
The scaling process is transparent, i.e. the solution to the original problem is reported. It is important
to be aware that the optimizer terminates when the termination criterion is met on the scaled problem,
therefore significant primal or dual infeasibilities may occur after unscaling for badly scaled problems.
The best solution to this problem is to reformulate it, making it better scaled.
By default MOSEK heuristically chooses a suitable scaling. The scaling for interior-point and simplex
optimizers can be controlled with the parameters MSK IPAR INTPNT SCALING and MSK IPAR SIM SCALING
respectively.
5.1.4 Using multiple threads
The interior-point optimizers in MOSEK have been parallelized. This means that if you solve linear,
quadratic, conic, or general convex optimization problem using the interior-point optimizer, you can
take advantage of multiple CPU’s.
By default MOSEK will automatically select the number of threads to be employed when solving
the problem. However, the number of threads employed can be changed by setting the parameter
MSK IPAR NUM THREADS. This should never exceed the number of cores on the computer.
The speed-up obtained when using multiple threads is highly problem and hardware dependent, and
consequently, it is advisable to compare single threaded and multi threaded performance for the given
problem type to determine the optimal settings.
For small problems, using multiple threads is not be worthwhile and may even be counter productive.
5.2 Linear optimization
5.2.1 Optimizer selection
Two different types of optimizers are available for linear problems: The default is an interior-point
method, and the alternatives are simplex methods. The optimizer can be selected using the parameter
MSK IPAR OPTIMIZER.