This is a pre-release of the MosekCOModel project. It is provided with absolutely no official support and is still to be considered highly experimenental.

MosekCOModel

The MosekCOModel crate is a modeling package for building optimization models with Mosek.rs. The Mosek.rs package is a relatively thin interface in top of low-level MOSEK optimizer C API, where MosekModel is an attempt to create an interface that is more like the MOSEK Fusion modelling interface.

Published crates: https://crates.io/crates/mosekcomodel

Documentation for latest crates: https://docs.rs/mosekcomodel/latest/mosekcomodel/

Design principle

MosekModel allows building a model of the form

min/max   c^t x + c_fix
such that Ax_b ∊ K_c
          x ∊ K_x  

That is affine expressions and conic domains of constraints and variables.

The MosekModel package provides functionality to build the linear expressions.

Simple conic example

Implementing the models

minimize y₁ + y₂ + y₃
such that
         x₁ + x₂2 + 2.0 x₃ = 1.0
                  x₁,x₂,x₃ ≥ 0.0
and
         (y₁,x₁,x₂) in C₃,
         (y₂,y₃,x₃) in K₃

where C₃ and K₃ are respectively the quadratic and rotated quadratic cone of size 3 defined as

    C₃ = { z₁,z₂,z₃ :      z₁ ≥ √(z₂² + z₃²) }
    K₃ = { z₁,z₂,z₃ : 2 z1 z₂ ≥ z₃²          }

This is the included model cqo1.rs:

extern crate mosekcomodel;
use mosekcomodel::*;
use mosekcomodel::expr::*;

fn main() {
    let mut m = Model::new(Some("cqo1"));
    let x = m.variable(Some("x"), greater_than(vec![0.0;3]));
    let y = m.variable(Some("y"), 3);

    // Create the aliases
    //      z1 = [ y[0],x[0],x[1] ]
    //  and z2 = [ y[1],y[2],x[2] ]

    let z1 = Variable::vstack(&[&y.index(0..1), &x.index(0..2)]);
    let z2 = Variable::vstack(&[&y.index(1..3), &x.index(2..3)]);

    // Create the constraint
    //      x[0] + x[1] + 2.0 x[2] = 1.0
    let aval = &[1.0, 1.0, 2.0];
    let _ = m.constraint(Some("lc"), &aval.dot(x.clone()), equal_to(1.0));

    // Create the constraints
    //      z1 belongs to C_3
    //      z2 belongs to K_3
    // where C_3 and K_3 are respectively the quadratic and
    // rotated quadratic cone of size 3, i.e.
    //                 z1[0] >= sqrt(z1[1]^2 + z1[2]^2)
    //  and  2.0 z2[0] z2[1] >= z2[2]^2
    let qc1 = m.constraint(Some("qc1"), &z1, in_quadratic_cone(3));
    let _qc2 = m.constraint(Some("qc2"), &z2, in_rotated_quadratic_cone(3));

    // Set the objective function to (y[0] + y[1] + y[2])
    m.objective(Some("obj"), Sense::Minimize, &y.clone().sum());

    // Solve the problem
    m.solve();

    // Get the linear solution values
    let solx = m.primal_solution(SolutionType::Default,&x);
    let soly = m.primal_solution(SolutionType::Default,&y);
    println!("x = {:?}", solx);
    println!("y = {:?}", soly);

    // Get primal and dual solution of qc1
    let qc1lvl = m.primal_solution(SolutionType::Default,&qc1);
    let qc1sn  = m.dual_solution(SolutionType::Default,&qc1);

    println!("qc1 levels = {:?}", qc1lvl);
    println!("qc1 dual conic var levels = {:?}", qc1sn);
}

Compiling, testing, running

To compile the project and run basic tests, do

cargo build && cargo test

When running examples, the compiled examples cannot locate the MOSEK library

Running examples requires the MOSEK library to be available. The simplest solution is to download and unpack the MOSEK distro from https://www.mosek.com/downloads/, unpack the distro and set relevant environment variable:

• On MS Windows: set PATH=C:\full\path\to\mosek\binaries;%PATH%
• On Mac OSX: export DYLD_LIBRARY_PATH=/full/path/to/mosek/binaries:$DYLD_LIBRARY_PATH
• On Linux: export LD_LIBRARY_PATH=/full/path/to/mosek/binaries:$LD_LIBRARY_PATH