F. The solution file format


MOSEK provides one or two solution files depending on the problem type and the optimizer used. If a problem is optimized using the interior-point optimizer and no basis identification is required, then a file named probname.sol is provided. probname is the name of the problem and .sol is the file extension. If the problem is optimized using the simplex optimizer or basis identification is performed, then a file named probname.bas is created presenting the optimal basis solution. Finally, if the problem contains integer constrained variables then a file named probname.int is created. It contains the integer solution.

F.1. The basic and interior solution files

In general both the interior-point and the basis 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 statuses are shown. In this case the information shows that the problem is primal and dual feasible and the solution is optimal. Next the primal and dual objective values are displayed.

CONSTRAINTS

Subsequently in the constraint section the following information is listed for each constraint:

INDEX

A sequential index assigned to the constraint by MOSEK.

NAME

The name of the constraint assigned by the user.

AT

The status of the constraint. In Table F.1 the possible values of the status keys and their interpretation are shown.

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.
Table F.1: Status keys.

ACTIVITY

Given the ith constraint on the form

\begin{math}\nonumber{}l_{i}^{c}\leq{}\sum _{{j=1}}^{n}a_{{ij}}x_{j}\leq{}u_{i}^{c},\end{math} (F.1.1)

then activity denote the quantity [[MathCmd 655]], where [[MathCmd 269]] is the value for the x solution.

LOWER LIMIT

Is the quantity [[MathCmd 439]] (see (F.1.1)).

UPPER LIMIT

Is the quantity [[MathCmd 567]] (see (F.1.1)).

DUAL LOWER

Is the dual multiplier corresponding to the lower limit on the constraint.

DUAL UPPER

Is the dual multiplier corresponding to the upper limit on the constraint.

VARIABLES

The last section of the solution report lists information for the variables. This information has a similar interpretation as for the constraints. However, the column with the header [CONIC DUAL] is only included for problems having one or more conic constraints. This column shows the dual variables corresponding to the conic constraints.

F.2. The integer solution file

The integer solution is equivalent to the basic and interior solution files except that no dual information is included.

Wed Feb 29 16:20:50 2012