7.2 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.

7.2.1 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. 7.3 (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. 7.4 (Input/Output).

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

7.2.2 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.

7.2.3 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 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.get_pro_sta and Task.get_sol_sta, 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

7.2.4 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:

• Task.get_primal_obj, Task.get_dual_obj — the primal and dual objective value.

• Task.get_xx — solution values for the variables.

• Task.get_solution — a full solution with primal and dual values

and many more specialized methods, see the API reference.

7.2.5 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.

extern crate mosek;

use mosek::{Task,Streamtype,Solsta,Soltype};
use std::env;

const CQO1_PTF : &str = "Task 'CQO1 EXAMPLE'
Objective obj
    Minimize + x4 + x5 + x6
Constraints
    c1 [1] + x1 + x2 + 2 x3
Variables
    k1 [QUAD(3)]
        x4
        x1 [0;+inf]
        x2 [0;+inf]
    k2 [RQUAD(3)]
        x5
        x6
        x3 [0;+inf]
";


fn main() -> Result<(),String> {
    let args: Vec<String> = env::args().collect();

    let mut task = Task::new().unwrap().with_callbacks();
    if args.len() < 2 {
        task.read_ptf_string(CQO1_PTF)?;
    }
    else {
        task.read_data(args[1].as_str())?;
    }

    // Perform optimization.
    let trm = task.optimize()?;
    task.solution_summary(Streamtype::LOG)?;

    // Handle solution status. We expect Optimal
    let solsta = task.get_sol_sta(Soltype::ITR)?;

    match solsta {
        Solsta::OPTIMAL => {
            // Fetch and print the solution
            println!("An optimal interior point solution is located.");
            let numvar = task.get_num_var()?;
            let mut xx = vec![0.0; numvar as usize];
            task.get_xx(Soltype::ITR, xx.as_mut_slice())?;
            println!("xx = {:?}",xx)
        },
        Solsta::DUAL_INFEAS_CER =>
          println!("Dual infeasibility certificate found."),
        Solsta::PRIM_INFEAS_CER =>
          println!("Primal infeasibility certificate found."),
        Solsta::UNKNOWN => {
          // The solutions status is unknown. The termination code
          // indicates why the optimizer terminated prematurely.
          println!("The solution status is unknown.");
          let (symname,desc) = mosek::get_code_desc(trm)?;
          println!("   Termination code: {} {}\n", symname, desc)
        },
        _ =>
          println!("Unexpected solution status {}\n",solsta)
    }
    Ok(())
}