The MOSEK command line tool Version 7.0 (Revision 141)

6.7. UNDERSTANDING SOLUTION QUALITY 55
• Improve the formulation: A mixed-integer optimization problem may be impossible to solve
in one form and quite easy in another form. However, it is beyond the scope of this manual
to discuss good formulations for mixed-integer problems. For discussions on this topic see for
example [11].
6.7 Understanding solution quality
To determine the quality of the solution one should check the following:
• The solution status key returned by MOSEK.
• The optimality gap: A measure for how much the located solution can deviate from the optimal
solution to the problem.
• Feasibility. How much the solution violates the constraints of the problem.
The optimality gap is a measure for how close the solution is to the optimal solution. The optimality
gap is given by
ɛ = |(objective value of feasible solution) − (objective bound)|.
The objective value of the solution is guarantied to be within ɛ of the optimal solution.
The optimality gap can be retrieved through the solution item MSK DINF MIO OBJ ABS GAP. Often it is
more meaningful to look at the optimality gap normalized with the magnitude of the solution. The
relative optimality gap is available in MSK DINF MIO OBJ REL GAP.