The MOSEK Python optimizer API manual Version 7.0 (Revision 141)
Optimizer API for Python - Documentation - Mosek Optimizer API for Python - Documentation - Mosek
170 CHAPTER 13. THE ANALYZERS • Removing suspected constraints from the problem. Returning to the transportation example, we discover that removing the fifth constraint makes the problem feasible. x 12 = 200 13.2.3 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. 13.2.3.1 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. 13.2.4 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 iparam.infeas report auto to onoffkey.on. This causes MOSEK to print a report on variables and constraints involved in the infeasibility.
13.2. ANALYZING INFEASIBLE PROBLEMS 171 The iparam.infeas report level parameter controls the amount of information presented in the infeasibility report. The default value is 1 . 13.2.4.1 Example: Primal infeasibility We will reuse the example (13.1) located in infeas.lp: \ \ An example of an infeasible linear problem. \ minimize obj: + 1 x11 + 2 x12 + 1 x13 + 4 x21 + 2 x22 + 5 x23 + 4 x31 + 1 x32 + 2 x33 st s0: + x11 + x12
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13.2. ANALYZING INFEASIBLE PROBLEMS 171<br />
<strong>The</strong> iparam.infeas report level parameter controls the amount of information presented in the<br />
infeasibility report. <strong>The</strong> default value is 1 .<br />
13.2.4.1 Example: Primal infeasibility<br />
We will reuse the example (13.1) located in infeas.lp:<br />
\<br />
\ An example of an infeasible linear problem.<br />
\<br />
minimize<br />
obj: + 1 x11 + 2 x12 + 1 x13<br />
+ 4 x21 + 2 x22 + 5 x23<br />
+ 4 x31 + 1 x32 + 2 x33<br />
st<br />
s0: + x11 + x12
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