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 a response code of type rescode, relevant for error handling. It indicates if any errors occurred in any phase of optimization (including processing input data). It will also indicate system-related errors (such as an out of memory error, licensing error etc.). Finally, it will also indicate if the optimizer terminated correctly, but for a non-standard reason, for example because it reached a time limit or met another criterion set by the user. Such termination codes are not errors. The expected value for a typical successful optimization without any special settings is "MSK_RES_OK".
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:
Simplex optimizer |
Interior-point optimizer |
Mixed-integer optimizer |
|
Linear problem |
|
|
|
Nonlinear continuous problem |
|
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Problem with integer variables |
|
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
"MSK_PRO_STA_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 (
"MSK_SOL_STA_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 fields prosta and solsta of a solution structure solution_info, for instance r$sol$itr$prosta, r$sol$itr$solsta for the interior-point solution.
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.
Outcome |
Problem status |
Solution status |
|---|---|---|
Optimal |
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Primal infeasible |
||
Dual infeasible (unbounded) |
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Uncertain (stall, numerical issues, etc.) |
Outcome |
Problem status |
Solution status |
|---|---|---|
Integer optimal |
||
Infeasible |
||
Integer feasible point |
||
No conclusion |
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:
r$sol$itr$pobjval,r$sol$itr$dobjval— the primal and dual objective value.r$sol$itr$xx— solution values for the variables.r$sol$itr$y,r$sol$itr$slxand so on — dual values for the linear constraints
and many other fields of the solution_info structure (replace itr with bas or int for other solution types). Note that if the optimization failed then the r$sol field may not exist and attempting to access it will cause an error.
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.
response <- function()
{
# In this example we set up a simple problem
prob <- setupProblem()
# (Optionally) Uncomment the next line to get solution status Unknown
# prob$iparam <- list(INTPNT_MAX_ITERATIONS=1)
# Perform the optimization.
r <- mosek(prob, list(verbose=0))
# Use the line below instead to get more log output
#r <- mosek(prob, list(verbose=10))
# Expected result: The solution status of the interior-point solution is optimal.
# Check if there was a fatal error
if (r$response$code != 0 && startsWith(r$response$msg, "MSK_RES_ERR"))
{
print(sprintf("Optimization error: %s (%d),", r$response$msg, r$response$code))
}
else
{
if (r$sol$itr$solsta == 'OPTIMAL')
{
print('An optimal interior-point solution is located:')
print(r$sol$itr$xx)
}
else if (r$sol$itr$solsta == 'DUAL_INFEASIBLE_CER')
{
print('Dual infeasibility certificate found.')
}
else if (r$sol$itr$solsta == 'PRIMAL_INFEASIBLE_CER')
{
print('Primal infeasibility certificate found.')
}
else if (r$sol$itr$solsta == 'UNKNOWN')
{
# The solutions status is unknown. The termination code
# indicates why the optimizer terminated prematurely.
print('The solution status is unknown.')
print(sprintf('Termination code: %s (%d).', r$response$msg, r$response$code))
}
else
{
printf('An unexpected solution status is obtained.')
}
}
}
