The MOSEK command line tool Version 7.0 (Revision 141)

5.1. HOW AN OPTIMIZER WORKS 35
5.1.1.2 Eliminator
The purpose of the eliminator is to eliminate free and implied free variables from the problem using
substitution. For instance, given the constraints
y = ∑ x j ,
y, x ≥ 0,
y is an implied free variable that can be substituted out of the problem, if deemed worthwhile.
If the eliminator consumes too much time or memory compared to the reduction in problem size
gained it may be disabled. This can be done with the parameter MSK IPAR PRESOLVE ELIMINATOR USE
to MSK OFF.
In rare cases the eliminator may cause that the problem becomes much hard to solve.
5.1.1.3 Linear dependency checker
The purpose of the linear dependency check is to remove linear dependencies among the linear equalities.
For instance, the three linear equalities
x 1 + x 2 + x 3 = 1,
x 1 + 0.5x 2 = 0.5,
0.5x 2 + x 3 = 0.5
contain exactly one linear dependency. This implies that one of the constraints can be dropped without
changing the set of feasible solutions. Removing linear dependencies is in general a good idea since it
reduces the size of the problem. Moreover, the linear dependencies are likely to introduce numerical
problems in the optimization phase.
It is best practise to build models without linear dependencies. If the linear dependencies are removed
at the modeling stage, the linear dependency check can safely be disabled by setting the parameter
MSK IPAR PRESOLVE LINDEP USE to MSK OFF.
5.1.2 Dualizer
All linear, conic, and convex optimization problems have an equivalent dual problem associated with
them. MOSEK has built-in heuristics to determine if it is most efficient to solve the primal or dual
problem. The form (primal or dual) solved is displayed in the MOSEK log. Should the internal
heuristics not choose the most efficient form of the problem it may be worthwhile to set the dualizer
manually by setting the parameters:
• MSK IPAR INTPNT SOLVE FORM: In case of the interior-point optimizer.
• MSK IPAR SIM SOLVE FORM: In case of the simplex optimizer.
Note that currently only linear problems may be dualized.