7.1 Accessing the solution

This section contains important information about the status of the solver and the status of the solution, which must be checked in order to properly interpret the results of the optimization.

7.1.1 Solver termination

The optimizer provides two status codes relevant for error handling:

  • Response code of type rescode. It indicates if any unexpected error (such as an out of memory error, licensing error etc.) has occurred. The expected value for a successful optimization is rescode.ok.
  • Termination code: It provides information about why the optimizer terminated, for instance if a predefined time limit has been reached. These are not errors, but ordinary events that can be expected (depending on parameter settings and the type of optimizer used).

If the optimization was successful then the method Task.optimize returns normally and its output is the termination code. If an error occurs then the method throws an exception, which contains the response code. See Sec. 7.2 (Errors and exceptions) for how to access it.

If a runtime error causes the program to crash during optimization, the first debugging step is to enable logging and check the log output. See Sec. 7.3 (Input/Output).

If the optimization completes successfully, the next step is to check the solution status, as explained below.

7.1.2 Available solutions

MOSEK uses three kinds of optimizers and provides three types of solutions:

  • basic solution (BAS, from the simplex optimizer),
  • interior-point solution (ITR, from the interior-point optimizer),
  • integer solution (ITG, from the mixed-integer optimizer).

Under standard parameters settings the following solutions will be available for various problem types:

Table 3 Types of solutions available from MOSEK
  Simplex optimizer Interior-point optimizer Mixed-integer optimizer
Linear problem soltype.bas soltype.itr  
Nonlinear continuous problem   soltype.itr  
Problem with integer variables     soltype.itg

For linear problems the user can force a specific optimizer choice making only one of the two solutions available. For example, if the user disables basis identification, then only the interior point solution will be available for a linear problem. Numerical issues may cause one of the solutions to be unknown even if another one is feasible.

Not all components of a solution are always available. For example, there is no dual solution for integer problems.

The user will always need to specify which solution should be accessed.

7.1.3 Problem and solution status

Assuming that the optimization terminated without errors, the next important step is to check the problem and solution status. There is one for every type of solution, as explained above.

Problem status

Problem status (prosta, retrieved with Task.getprosta) determines whether the problem is certified as feasible. Its values can roughly be divided into the following broad categories:

  • feasible — the problem is feasible. For continuous problems and when the solver is run with default parameters, the feasibility status should ideally be prosta.prim_and_dual_feas.
  • primal/dual infeasible — the problem is infeasible or unbounded or a combination of those. The exact problem status will indicate the type of infeasibility.
  • unknown — the solver was unable to reach a conclusion, most likely due to numerical issues.

Solution status

Solution status (solsta, retrieved with Task.getsolsta) provides the information about what the solution values actually contain. The most important broad categories of values are:

  • optimal (solsta.optimal) — the solution values are feasible and optimal.
  • near optimal (solsta.near_optimal) — the solution values are feasible and they were certified to be at least nearly optimal up to some accuracy.
  • certificate — the solution is in fact a certificate of infeasibility (primal or dual, depending on the solution).
  • unknown/undefined — the solver could not solve the problem or this type of solution is not available for a given problem.

The solution status determines the action to be taken. For example, in some cases a suboptimal solution may still be valuable and deserve attention. It is the user’s responsibility to check the status and quality of the solution.

Typical status reports

Here are the most typical optimization outcomes described in terms of the problem and solution statuses. Note that these do not cover all possible situations that can occur.

Table 4 Continuous problems (solution status for soltype.itr or soltype.bas)
Outcome Problem status Solution status
Optimal prosta.prim_and_dual_feas solsta.optimal
Primal infeasible prosta.prim_infeas solsta.prim_infeas_cer
Dual infeasible prosta.dual_infeas solsta.dual_infeas_cer
Uncertain (stall, numerical issues, etc.) prosta.unknown solsta.unknown
Table 5 Integer problems (solution status for soltype.itg, others undefined)
Outcome Problem status Solution status
Integer optimal prosta.prim_feas solsta.integer_optimal
Infeasible prosta.prim_infeas solsta.unknown
Integer feasible point prosta.prim_feas solsta.prim_feas
No conclusion prosta.unknown solsta.unknown

7.1.4 Retrieving solution values

After the meaning and quality of the solution (or certificate) have been established, we can query for the actual numerical values. They can be accessed with methods such as:

and many more specialized methods, see the API reference.

7.1.5 Source code example

Below is a source code example with a simple framework for assessing and retrieving the solution to a conic quadratic optimization problem.

Listing 14 Sample framework for checking optimization result. Click here to download.
import mosek
import sys

# A log message
def streamprinter(text):
    sys.stdout.write(text)
    sys.stdout.flush()

def main(args):
  filename = args[0] if len(args) >= 1 else "../data/cqo1.mps"

  try:
    # Create environment and task
    with mosek.Env() as env:
      with env.Task(0, 0) as task:
        # (Optional) set a log stream
        # task.set_Stream(mosek.streamtype.log, streamprinter)

        # (Optional) uncomment to see what happens when solution status is unknown
        #task.putintparam(mosek.iparam.intpnt_max_iterations, 1)

        # In this example we read data from a file
        task.readdata(filename)

        # Optimize
        trmcode = task.optimize()

        # We expect solution status OPTIMAL
        solsta = task.getsolsta(mosek.soltype.itr)

        if solsta in [mosek.solsta.optimal,
                      mosek.solsta.near_optimal]:
          # Optimal solution. Fetch and print it.
          print("An optimal interior-point solution is located.")
          numvar = task.getnumvar()
          xx = [ 0.0 ] * numvar
          task.getxx(mosek.soltype.itr, xx)
          for i in range(numvar): 
            print("x[{0}] = {1}".format(i, xx[i]))

        elif solsta in [mosek.solsta.dual_infeas_cer,
                        mosek.solsta.near_dual_infeas_cer]:
          print("Dual infeasibility certificate found.")

        elif solsta in [mosek.solsta.prim_infeas_cer,
                        mosek.solsta.near_prim_infeas_cer]:
          print("Primal infeasibility certificate found.")
        
        elif solsta == mosek.solsta.unknown:
          # The solutions status is unknown. The termination code
          # indicates why the optimizer terminated prematurely.
          print("The solution status is unknown.")
          symname, desc = mosek.Env.getcodedesc(trmcode)
          print("   Termination code: {0} {1}".format(symname, desc))

        else:
          print("An unexpected solution status {0} is obtained.".format(str(solsta)))

  except mosek.Error as e:
      print("Unexpected error ({0}) {1}".format(e.errno, e.msg))

if __name__ == '__main__':
    main(sys.argv[1:])