Mosek.jl

Interface to the MOSEK solver for Julia.

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

• All relevant MOSEK C API functions are available
• Callbacks for information retrival and log output during optimization

MOSEK can solve LP (linear), Conic (second order conic, power, exponential etc.), SDP (semi-definite), QP (quadratic objective, quadratic constraints), and MIP (mixed-integer problems). These can be mixed as follows:

• LP+CONIC+SDP
• LP+CONIC+MIP

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

Documentation

All functions and constants in the Mosek.jl are briefly documented in docs strings, accessible assume

julia> import Mosek
julia> ?Mosek.putarowslice
  Replaces all elements in several rows the linear constraint matrix.

  putarowslice(task::MSKtask,first::Int32,last::Int32,ptrb::Vector{Int64},ptre::Vector{Int64},asub::Vector{Int32},aval::Vector{Float64})
  putarowslice(task::MSKtask,first::T0,last::T1,ptrb::T2,ptre::T3,asub::T4,aval::T5) where {T0<:Integer,T1<:Integer,T2<:AbstractVector{<:Integer},T3<:AbstractVector{<:Integer},T4<:AbstractVector{<:Integer},T5<:AbstractVector{<:Number}} 
  putarowslice(task::MSKtask,first::T0,last::T1,At:: SparseMatrixCSC{Float64})

  Arguments: 

  At::SparseMatrixCSC{{Float64} Transposed matrix defining the row values. Note that for efficiency reasons the *columns* of this matrix defines the *rows* to be replaced
  asub::Vector{Int32} Column indexes of new elements.
  aval::Vector{Float64} Coefficient values.
  first::Int32 First row in the slice.
  last::Int32 Last row plus one in the slice.
  ptrb::Vector{Int64} Array of pointers to the first element in the rows.
  ptre::Vector{Int64} Array of pointers to the last element plus one in the rows.
  task::MSKtask An optimization task.

For a more complete manual and full API reference, please refer to the MOSEK Julia API documentation.

Installation

Use the Julia package manager to install Mosek.jl:

Pkg.add("Mosek")

The Mosek.jl package requires the MOSEK distribution binaries run. Upon installation it will attempt to either local an installed MOSEK or download and install from the MOSEK website (www.mosek.com):

1. If the environment variable MOSEKBINDIR is defined, the installer will assume that this directory contains the necessary libraries. If it does not, the installer will fail.
2. If the current Mosek.jl installation uses a user-defined MOSEK and this is a valid version, this will be used.
3. If MOSEK is installed in the default location in the users HOME directory, and this installation has the correct version, this will be used.
4. If no usable MOSEK installation is found here, the installer will attempt to download and unpack the latest distro. In this case doing Pkg.build("Mosek") will update the MOSEK distro if possible.`

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

Pkg.build("Mosek")

If you have previously installed Mosek.jl using a pre-installed MOSEK distro, setting the MOSEKJL_FORCE_DOWNLOAD=YES will force the installer to download MOSEK from the web instead of using the old version.

Note that environment variables can be set temporarily from Julia as

ENV["MOSEKBINDIR"] = "/home/myname/lib"

Furthermore, a license file is required to use MOSEK (these are free for academic use). MOSEK will look first for the enironment variable MOSEKLM_LICENSE_FILE which, if defined, must point to the relevant license file. If this is not defined, MOSEK will look for a file called mosek.lic in the default install path, e.g.

$HOME/mosek/mosek.lic

Updating the Mosek library

If the MOSEK distro was installed manually, it can be updated simply by installing a newer distro in the same place. Otherwise, doing Pkg.build("Mosek") will check the latest MOSEK distro and update if possible.

You can see if the MOSEK distro was installed internally this way:

is_internal = open(joinpath(Pkg.dir("Mosek"),"deps","inst_method"),"r") do f readstring(f) == "internal" end

Use with JuMP

The MathOptInterface wrapper for MOSEK is a separate package called MosekTools. However, for consistency the optimizer is still named Mosek.Optimizer.

Use MOSEK with JuMP as follows:

using JuMP, MosekTools
model = Model(Mosek.Optimizer)

Note on versions and release

Since the Mosek.jl package is designed to match a specific MOSEK version (major+minor version), there are branches for the different MOSEK versions:

• Branch b0.8 is compatible with MOSEK 8.0. Not actively updated.
• Branch b0.9 is compatible with MOSEK 8.1. Currently updated only for bugfixes.
• Branch b1.1-msk9.1 is compatible with MOSEK 9.1. Not actively updated.
• Branch b1.1-msk9.2 is compatible with MOSEK 9.2. Not actively updated.
• Branch b1.1-msk9.3 is compatible with MOSEK 9.3. Currently updated only for bugfixes.
• From MOSEK 10.0 and forward, Mosek.jl branch bX.Y is compatible with MOSEK version X.Y.
• For MOSEK beta releases, there will be a corresponding branch, but there will not be releases of Mosek.jl for MOSEK beta releases. Mosek.jl release vX.Y.Z will be taken from branch bX.Y.