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 from the simplex optimizer,

  • interior-point solution from the interior-point optimizer,

  • integer solution from the mixed-integer optimizer.

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

Table 7.1 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 and no dual conic variables from the simplex optimizer.

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) 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) 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.

  • 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.

Problem and solution status for each solution can be retrieved with Task.getprosta and Task.getsolsta, respectively.

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 7.2 Continuous problems (solution status for interior-point and basic solution)

Outcome

Problem status

Solution status

Optimal

prosta.prim_and_dual_feas

solsta.optimal

Primal infeasible

prosta.prim_infeas

solsta.prim_infeas_cer

Dual infeasible (unbounded)

prosta.dual_infeas

solsta.dual_infeas_cer

Uncertain (stall, numerical issues, etc.)

prosta.unknown

solsta.unknown

Table 7.3 Integer problems (solution status for integer solution, 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 using:

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 optimization problem.

Listing 7.1 Sample framework for checking optimization result. Click here to download.
using System;
using mosek;
using System.Text;

namespace mosek.example
{
  // A log handler class
  class msgclass : mosek.Stream
  {
    public msgclass () {}
    public override void streamCB (string msg) { Console.Write ("{0}", msg); }
  }

  public class response
  {
    public static void Main(string[] argv)
    {
      StringBuilder symname = new StringBuilder();
      StringBuilder desc = new StringBuilder();

      string filename;
      if (argv.Length >= 1) filename = argv[0];
      else                  filename = "../data/cqo1.mps";

      // Define environment and task
      using (Env env = new Env())
      {
        using (Task task = new Task(env, 0, 0))
        {
          try 
          {
            // (Optionally) set a log handler
            // task.set_Stream (streamtype.log, new msgclass ());

            // (Optionally) uncomment this to get solution status unknown
            // task.putintparam(iparam.intpnt_max_iterations, 1);

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

            // Perform optimization
            rescode trm = task.optimize();
            task.solutionsummary(streamtype.log);

            // Handle solution status. We expect Optimal
            solsta solsta = task.getsolsta(soltype.itr);

            switch ( solsta )
            {
              case solsta.optimal:
                // Optimal solution. Print variable values
                Console.WriteLine("An optimal interior-point solution is located.");
                int numvar = task.getnumvar();
                double[] xx = new double[numvar];
                task.getxx(soltype.itr, xx);
                for(int i = 0; i < numvar; i++) 
                  Console.WriteLine("x[" + i + "] = " + xx[i]);
                break;

              case solsta.dual_infeas_cer:
                Console.WriteLine("Dual infeasibility certificate found.");
                break;

              case solsta.prim_infeas_cer:
                Console.WriteLine("Primal infeasibility certificate found.");
                break;

              case solsta.unknown:
                /* The solutions status is unknown. The termination code
                   indicates why the optimizer terminated prematurely. */
                Console.WriteLine("The solution status is unknown.");
                Env.getcodedesc(trm, symname, desc);
                Console.WriteLine("  Termination code: {0} {1}", symname, desc);
                break;

              default:
                Console.WriteLine("An unexpected solution status " + solsta);
                break;
            }
          }
          catch (mosek.Error e)
          {
            Console.WriteLine("Unexpected optimization error ({0}) {1}", e.Code, e.Message);
          }
        }
      }
    }
  }
}