The MOSEK command line tool Version 7.0 (Revision 141)

64 CHAPTER 7. THE ANALYZERS
makes the problem feasible.
7.2.3 Locating the cause of dual infeasibility
A problem may also be dual infeasible. In this case the primal problem is often unbounded, mening
that feasbile solutions exists such that the objective tends towards infinity. An example of a dual
infeasible and primal unbounded problem is:
minimize x 1
subject to x 1 ≤ 5.
To resolve a dual infeasibility the primal problem must be made more restricted by
• Adding upper or lower bounds on variables or constraints.
• Removing variables.
• Changing the objective.
7.2.3.1 A cautious note
The problem
minimize 0
subject to 0 ≤ x 1 ,
x j ≤ x j+1 , j = 1, . . . , n − 1,
x n ≤ − 1
is clearly infeasible. Moreover, if any one of the constraints are dropped, then the problem becomes
feasible.
This illustrates the worst case scenario that all, or at least a significant portion, of the constraints are
involved in the infeasibility. Hence, it may not always be easy or possible to pinpoint a few constraints
which are causing the infeasibility.
7.2.4 The infeasibility report
MOSEK includes functionality for diagnosing the cause of a primal or a dual infeasibility. It can be
turned on by setting the MSK IPAR INFEAS REPORT AUTO to MSK ON. This causes MOSEK to print a
report on variables and constraints involved in the infeasibility.
The MSK IPAR INFEAS REPORT LEVEL parameter controls the amount of information presented in the
infeasibility report. The default value is 1 .