The MOSEK command line tool Version 7.0 (Revision 141)

8.5. SENSITIVITY ANALYSIS WITH THE COMMAND LINE TOOL 75
The linearity intervals and shadow prices for u c i , lx j , and ux j are computed similarly to lc i .
The left and right shadow prices for c j denoted σ 1 and σ 2 respectively are computed as follows:
and
σ 1 = minimize e T j x
subject to l c + βe i ≤ Ax ≤ u c ,
c T x = z ∗ ,
l x ≤ x ≤ u x
σ 2 = maximize e T j x
subject to l c + βe i ≤ Ax ≤ u c ,
c T x = z ∗ ,
l x ≤ x ≤ u x .
Once again the above two optimization problems make it easy to interpret the shadow prices. Indeed,
if x ∗ is an arbitrary primal optimal solution, then
x ∗ j ∈ [σ 1 , σ 2 ].
The linearity interval [β 1 , β 2 ] for a c j is computed as follows:
and
β 1 = minimize β
subject to A T (s c l − s c u) + s x l − s x u = c + βe j ,
(l c ) T (s c l ) − (u c ) T (s c u) + (l x ) T (s x l ) − (u x ) T (s x u) − σ 1 β ≤ z ∗ ,
s c l , s c u, s c l , s x u ≥ 0
β 2 = maximize β
subject to A T (s c l − s c u) + s x l − s x u = c + βe j ,
(l c ) T (s c l ) − (u c ) T (s c u) + (l x ) T (s x l ) − (u x ) T (s x u) − σ 2 β ≤ z ∗ ,
s c l , s c u, s c l , s x u ≥ 0.
8.5 Sensitivity analysis with the command line tool
A sensitivity analysis can be performed with the MOSEK command line tool using the command
mosek myproblem.mps -sen sensitivity.ssp
where sensitivity.ssp is a file in the format described in the next section. The ssp file describes
which parts of the problem the sensitivity analysis should be performed on.
By default results are written to a file named myproblem.sen.
changed by setting the
MSK SPAR SENSITIVITY RES FILE NAME
If necessary, this filename can be