The MOSEK command line tool Version 7.0 (Revision 141)

5.2. LINEAR OPTIMIZATION 43
• Raise tolerances for allowed primal or dual feasibility: Hence, increase the value of
– MSK DPAR BASIS TOL X, and
– MSK DPAR BASIS TOL S.
• Raise or lower pivot tolerance: Change the MSK DPAR SIMPLEX ABS TOL PIV parameter.
• Switch optimizer: Try another optimizer.
• Switch off crash: Set both MSK IPAR SIM PRIMAL CRASH and MSK IPAR SIM DUAL CRASH to 0.
• Experiment with other pricing strategies: Try different values for the parameters
– MSK IPAR SIM PRIMAL SELECTION and
– MSK IPAR SIM DUAL SELECTION.
• If you are using hot-starts, in rare cases switching off this feature may improve stability. This is
controlled by the MSK IPAR SIM HOTSTART parameter.
• Increase maximum set-backs allowed controlled by MSK IPAR SIM MAX NUM SETBACKS.
• If the problem repeatedly becomes infeasible try switching off the special degeneracy handling.
See the parameter MSK IPAR SIM DEGEN for details.
5.2.4 The interior-point or the simplex optimizer?
Given a linear optimization problem, which optimizer is the best: The primal simplex, the dual simplex
or the interior-point optimizer?
It is impossible to provide a general answer to this question, however, the interior-point optimizer
behaves more predictably — it tends to use between 20 and 100 iterations, almost independently of
problem size — but cannot perform hot-start, while simplex can take advantage of an initial solution,
but is less predictable for cold-start. The interior-point optimizer is used by default.
5.2.5 The primal or the dual simplex variant?
MOSEK provides both a primal and a dual simplex optimizer. Predicting which simplex optimizer
is faster is impossible, however, in recent years the dual optimizer has seen several algorithmic and
computational improvements, which, in our experience, makes it faster on average than the primal
simplex optimizer. Still, it depends much on the problem structure and size.
Setting the MSK IPAR OPTIMIZER parameter to MSK OPTIMIZER FREE SIMPLEX instructs MOSEK to
choose which simplex optimizer to use automatically.
To summarize, if you want to know which optimizer is faster for a given problem type, you should try
all the optimizers.