6.1 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.

6.1.1 Solver termination

If an error occurs during optimization then an exception will be raised. More about errors and exceptions in Sec. 6.2 (Errors and exceptions).

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. 6.3 (Input/Output).

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

6.1.2 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 6.1 Types of solutions available from MOSEK

	Simplex optimizer	Interior-point optimizer	Mixed-integer optimizer
Linear problem	basic	interior
Nonlinear continuous problem		interior
Problem with integer variables			integer

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.

6.1.3 Problem and solution status

Assuming that the optimization terminated without errors, the next important step is to check the problem and solution status and availability of solutions. 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 "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 ("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 can be found in the outputs prosta and solsta of mosekmodel.hassolution.

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

Outcome	Problem status	Solution status
Optimal	"PRIM_AND_DUAL_FEAS"	"OPTIMAL"
Primal infeasible	"PRIM_INFEAS"	"PRIM_INFEAS_CER"
Dual infeasible (unbounded)	"DUAL_INFEAS"	"DUAL_INFEAS_CER"
Uncertain (stall, numerical issues, etc.)	"UNKNOWN"	"UNKNOWN"

Table 6.3 Integer problems (solution status for integer solution, others undefined)

Outcome	Problem status	Solution status
Integer optimal	"PRIM_FEAS"	"INTEGER_OPTIMAL"
Infeasible	"PRIM_INFEAS"	"UNKNOWN"
Integer feasible point	"PRIM_FEAS"	"PRIM_FEAS"
No conclusion	"UNKNOWN"	"UNKNOWN"

6.1.4 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:

• mosekmodel.getsolution — the primal or dual solution values for arguments x and y, respectively.

6.1.5 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 6.1 Sample framework for checking optimization result. Click here to download.

    % Solve the model
    try
        model.solve();
    catch ME
        warning("An error during optimization; handle it here.");
        rethrow(ME);
    end
    
    % We check if the interior-point solution exists and what status it has
    [exists, prosta, solsta] = model.hassolution("interior");

    if exists
        disp("Solved the problem with statuses:");
        disp(prosta);
        disp(solsta);

        switch solsta
            case "OPTIMAL"
                disp("Optimal solution found:");
                x = model.getsolution("interior");
                disp(x);
            case "PRIM_INFEAS_CER"
                disp("The problem is primal infeasible.");
            case "DUAL_INFEAS_CER"
                disp("The problem is dual infeasible.");
            case "UNKNOWN"
                disp("Solution status UNKNOWN. This could indicate numerical issues");
            default
                disp("Another solution status:")
                disk(solsta)
        end
    else
        warning("Solution does not exists");
    end