15.8 The Solution File Format¶
MOSEK provides several solution files depending on the problem type and the optimizer used:
basis solution file (extension
.bas
) if the problem is optimized using the simplex optimizer or basis identification is performed,interior solution file (extension
.sol
) if a problem is optimized using the interior-point optimizer and no basis identification is required,integer solution file (extension
.int
) if the problem contains integer constrained variables.
All solution files have the format:
NAME : <problem name>
PROBLEM STATUS : <status of the problem>
SOLUTION STATUS : <status of the solution>
OBJECTIVE NAME : <name of the objective function>
PRIMAL OBJECTIVE : <primal objective value corresponding to the solution>
DUAL OBJECTIVE : <dual objective value corresponding to the solution>
CONSTRAINTS
INDEX NAME AT ACTIVITY LOWER LIMIT UPPER LIMIT DUAL LOWER DUAL UPPER
? <name> ?? <a value> <a value> <a value> <a value> <a value>
VARIABLES
INDEX NAME AT ACTIVITY LOWER LIMIT UPPER LIMIT DUAL LOWER DUAL UPPER CONIC DUAL
? <name> ?? <a value> <a value> <a value> <a value> <a value> <a value>
In the example the fields ?
and <>
will be filled with problem and solution specific information. As can be observed a solution report consists of three sections, i.e.
HEADER
In this section, first the name of the problem is listed and afterwards the problem and solution status are shown. Next the primal and dual objective values are displayed.
CONSTRAINTS
For each constraint \(i\) of the form
the following information is listed:
INDEX
: A sequential index assigned to the constraint by MOSEKNAME
: The name of the constraint assigned by the user.AT
: The status of the constraint. In Table 15.4 the possible values of the status keys and their interpretation are shown.Table 15.4 Status keys.¶ Status key
Interpretation
UN
Unknown status
BS
Is basic
SB
Is superbasic
LL
Is at the lower limit (bound)
UL
Is at the upper limit (bound)
EQ
Lower limit is identical to upper limit
**
Is infeasible i.e. the lower limit is greater than the upper limit.
ACTIVITY
: the quantity \(\sum_{j=1}^n a_{ij} x_j^*\) , where \(x^*\) is the value of the primal solution.LOWER LIMIT
: the quantity \(l_i^c\) (see (15.15).)UPPER LIMIT
: the quantity \(u_i^c\) (see (15.15).)DUAL LOWER
: the dual multiplier corresponding to the lower limit on the constraint.DUAL UPPER
: the dual multiplier corresponding to the upper limit on the constraint.
VARIABLES
The last section of the solution report lists information about the variables. This information has a similar interpretation as for the constraints. However, the column with the header
CONIC DUAL
is included for problems having one or more conic constraints. This column shows the dual variables corresponding to the conic constraints.
Example: lo1.sol
In Listing 15.7 we show the solution file for the lo1.opf
problem.