bstellato / Mosek.jl

Interface to the Mosek solver in Julia

Mosek.jl

Interface to the Mosek solver in Julia.

Mosek.jl is a more or less complete mapping of the MOSEK functionality:

• Most MOSEK C API functions are available
• Callbacks for information retrival and log output during optimization
• Interface for the MOSEK general convex solver
• Implementation of the LinprogSolver interface and other interfaces for JuMP (https://github.com/JuliaOpt/JuMP.jl)

MOSEK can solve LP (linear), SOCP (second order conic), SDP (semi-definite), QP (quadratic objective, quadratic constraints), GECO (general convex) and MIP (mixed-integer problems). These can be mixed as follows:

• LP+SOCP+SDP
• LP+SOCP+MIP
• LP+QP+MIP
• LP+QP+GECO

MOSEK is commercial software, but free licenses are available for academic use. See here for details.

Installation

Use the Julia package manager to install Mosek.jl:

Pkg.add("Mosek")

When installing, the installer will look for the MOSEK library in following places:

• First, if the environment variable MOSEKBINDIR is defined, it will look for the MOSEK library in the directory it points to. I.e. it must point the the bin/ directory in the MOSEK distro.
• Secondly, it will look for the MOSEK distribution in the user's home directory. This usually resolves to:
  • OS X: /Users/username
  • Linux: /home/username
  • Windows: C:\Users\username
• Thirdly, on Linux and OS X it will attempt to download MOSEK and install it in the Julia configuration directory.

If the MOSEK installation is moved it is necessary to rebuild the package using

Pkg.build("Mosek")

Furthermore, to run an optimization a license is required (these are free for academic use). Mosek will look first for the enironment variable MOSEKLM_LICENSE_FILE which must point to the relevant license file, and, if this is not present, it will look for a file called mosek.lic in the default install path.

Updating the Mosek library

If the MOSEK distro was installed manually, it can be updated simply by installing a newer distro.

If the Mosek.jl installer fetched and installed the MOSEK distro, it cannot automatically update, even when doing Pkg.update() or Pkg.build("Mosek"). Currently the simplest way to force the update is to do

Pkg.rm("Mosek") ; Pkg.add("Mosek") ; Pkg.build("Mosek")

If this is not desirable (e.g. because other packages depend on Mosek), you can remote the temporary files from the Mosek.jl installation. On Unix this is usually

rm -f ~/.julia/Mosek/downloads/*

Documentation

All functions and constants in the Mosek.jl are briefly documented here.

For a more complete description of functions, please refer to the MOSEK C API documentation.

The General Convex interface is not documented at all, but the example nlo1.jl show the general idea.

MathProgBase interface

Mosek implements the solver-independent MathProgBase interface, and so can be used within modeling software like JuMP. The solver object is called MosekSolver. Parameters are accepted and mirror the names in the Mosek documentation, except for the MSK_[I|D|S]PAR prefix. For example, you can suppress output by saying MosekSolver(LOG=0), where LOG corresponds to the MSK_IPAR_LOG parameter. The type of the parameter is inferred by the provided value.