Mosek¶

Mosek is a versatile linear, quadratic, quadratically constrained and conic optimizer that supports continuous and discrete variables. The framework used by the driver supports automatic reformulation for many expression types; the modeling guide can be found here.

How to use it¶

ampl: option solver mosek; # change the solver
ampl: option mosek_options 'option1=value1 option2=value2'; # specify options
ampl: solve; # solve the problem

How to install using amplpy:

# Install Python API for AMPL:
$ python -m pip install amplpy --upgrade

# Install AMPL & solver modules:
$ python -m amplpy.modules install mosek # install MOSEK

# Activate your license (e.g., free ampl.com/ce or ampl.com/courses licenses):
$ python -m amplpy.modules activate <your-license-uuid>

How to use:

from amplpy import AMPL
ampl = AMPL()
...
ampl.solve(solver="mosek", mosek_options="option1=value1 option2=value2")

Learn more about what we have to offer to implement and deploy Optimization in Python.

At a glance¶

Resources¶

Features¶

Problem types:
- LP, QP, QCP, conic programs (SOCP, exponential cones)
- MIP, MIQP, MIQCP, mixed-integer conic programs
Features for all models:
- Problem input
  - Basis IO
  - Warm start
- Model investigation
  - Sensitivity analysis
- Dealing with infeasibility/unboundedness
  - Unbounded rays
Features for MIP models:
- Model investigation
  - Return MIP gap
  - Return best dual bound

Solver options¶

Full list of solver options:

MOSEK Options

Many solver parameters can be changed directly from AMPL, by specifying them as a space separated string in the option mosek_options. A list of all supported options is available here or can be obtained by executing the solver driver with the -= command line parameter:

mosek -=

or from AMPL:

shell "mosek -=";

Solver options can have multiple aliases, to accomodate for different user types. The main numenclature is given first in the -= output, then followed by aliases in brackets, see for example the listing for lim:iter:

lim:iter (iterlim, iterlimit)
      Iteration limit (default: no limit).

The main numenclature contains a prefix (lim: in this case) to help categorize and find the options relevant to a context. To list only the options with a specific prefix (lim: for this example), run:

mosek -=lim:

More details on solver options: Features guide.

Specifying solver options and solving a model¶

After formulating the model in AMPL, execute the following to select Mosek as solver and pass the two options: return_mipgap=3 and outlev=1.

option solver mosek;
option mosek_options "retmipgap=3 outlev=1";
solve;

Retrieving solutions¶

The outcome of the last optimization is stored in the AMPL parameter solve_result_num and the relative message in solve_result.

display solve_result_num, solve_result;

Mosek solve result codes can be obtained by running mosek -! or ampl: shell "mosek -!";:

          0- 99 solved: optimal for an optimization problem, feasible for a satisfaction problem
        100-199 solved? solution candidate returned but error likely
            150 solved? MP solution check failed (option sol:chk:fail)
        200-299 infeasible
        300-349 unbounded, feasible solution returned
        350-399 unbounded, no feasible solution returned
        400-449 limit, feasible: stopped, e.g., on iterations or Ctrl-C
        450-469 limit, problem is either infeasible or unbounded
        470-499 limit, no solution returned
        500-999 failure, no solution returned
            550 failure: numeric issue, no feasible solution

For general information, see MP result codes guide.

Changelog¶

COPT Changelog

MOSEK Options