The MOSEK command line tool Version 7.0 (Revision 141)

6.5. TERMINATION CRITERION 53
The following parameters can be used to control the effort made by the integer optimizer to find an
initial feasible solution.
• MSK IPAR MIO HEURISTIC LEVEL: Controls how sophisticated and computationally expensive a
heuristic to employ.
• MSK DPAR MIO HEURISTIC TIME: The minimum amount of time to spend in the heuristic search.
• MSK IPAR MIO FEASPUMP LEVEL: Controls how aggressively the feasibility pump heuristic is used.
6.4.3 The optimization phase
This phase solves the problem using the branch and cut algorithm.
6.5 Termination criterion
In general, it is time consuming to find an exact feasible and optimal solution to an integer optimization
problem, though in many practical cases it may be possible to find a sufficiently good solution. Therefore,
the mixed-integer optimizer employs a relaxed feasibility and optimality criterion to determine
when a satisfactory solution is located.
A candidate solution that is feasible to the continuous relaxation is said to be an integer feasible
solution if the criterion
is satisfied.
min(|x j | − ⌊x j ⌋, ⌈x j ⌉ − |x j |) ≤ max(δ 1 , δ 2 |x j |) ∀j ∈ J
Whenever the integer optimizer locates an integer feasible solution it will check if the criterion
¯z − z ≤ max(δ 3 , δ 4 max(1, |¯z| ))
is satisfied. If this is the case, the integer optimizer terminates and reports the integer feasible solution
as an optimal solution. Please note that z is a valid lower bound determined by the integer optimizer
during the solution process, i.e.
z ≤ z ∗ .
The lower bound z normally increases during the solution process.
6.5.1 Relaxed termination
If an optimal solution cannot be located within a reasonable time, it may be advantageous to employ
a relaxed termination criterion after some time. Whenever the integer optimizer locates an integer feasible
solution and has spent at least the number of seconds defined by the MSK DPAR MIO DISABLE TERM TIME
parameter on solving the problem, it will check whether the criterion