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

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

Python

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.

Other APIs

AMPL APIs are interfaces that allow developers to access the features of the AMPL interpreter from within a programming language. We have APIs available for:

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 -!";:

Solve result table for MOSEK 10.2.0
	  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.
		Disable dual reductions or run IIS finder for definitive answer.
	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.