The MOSEK command line tool Version 7.0 (Revision 141)

6.3. THE MIXED-INTEGER CONIC OPTIMIZER 51
The mixed-integer conic optimizer is specialized for solving linear and conic optimization problems. It
can also solve pure quadratic and quadratically constrained problems, these problems are automatically
converted to conic problems before being solved. Whereas the mixed-integer optimizer deals with
quadratic and quadratically constrained problems directly.
The mixed-integer conic optimizer is run-to-run deterministic. This means that if a problem is solved
twice on the same computer with identical options then the obtained solution will be bit-for-bit identical
for the two runs. However, if a time limit is set then this may not be case since the time taken to solve
a problem is not deterministic. Moreover, the mixed-integer conic optimizer is parallelized i.e. it can
exploit multiple cores during the optimization. Finally, the mixed-integer conic optimizer is a free addon
to the continuous optimizers. However, for some linear problems the mixed-integer optimizer may
outperform the mixed-integer conic optimizer. On the other hand the mixed-integer conic optimizer
is included with continuous optimizers free of charge and usually the fastest for conic problems.
None of the mixed-integer optimizers handles symmetric matrix variables i.e semi-definite optimization
problems.
6.3 The mixed-integer conic optimizer
The mixed-integer conic optimizer is employed by setting the parameter MSK IPAR OPTIMIZER to
MSK OPTIMIZER MIXED INT CONIC.
The mixed-integer conic employs three phases:
Presolve:
In this phase the optimizer tries to reduce the size of the problem using preprocessing techniques.
Moreover, it strengthens the continuous relaxation, if possible.
Heuristic:
Using heuristics the optimizer tries to guess a good feasible solution.
Optimization:
The optimal solution is located using a variant of the branch-and-cut method.
6.3.1 Presolve
In the preprocessing stage redundant variables and constraints are removed. The presolve stage can
be turned off using the MSK IPAR MIO PRESOLVE USE parameter.
6.3.2 Heuristic
Initially, the integer optimizer tries to guess a good feasible solution using a heuristic.