Lib.rs

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#optimization #quadratic #linear #programming

osqp-rust

The OSQP (Operator Splitting Quadratic Program) solver

by Ed Barnard. Owned by Michael Stone.

1 unstable release

0.6.2 Mar 7, 2023

#1876 in Algorithms


Used in 2 crates

Apache-2.0

1.5MB
33K SLoC

Rust 25K SLoC // 0.0% comments C 6K SLoC // 0.3% comments Python 699 SLoC // 0.2% comments Bitbake 318 SLoC // 0.8% comments Shell 242 SLoC // 0.2% comments Batch 126 SLoC // 0.2% comments

osqp.rs

Rust wrapper for OSQP: the Operator Splitting QP Solver.

The OSQP (Operator Splitting Quadratic Program) solver is a numerical optimization package for solving problems in the form

minimize        0.5 x' P x + q' x

subject to      l <= A x <= u

where x in R^n is the optimization variable.

The objective function is defined by a positive semidefinite matrix P in S^n_+ and vector q in R^n.

The linear constraints are defined by matrix A in R^{m x n} and vectors l in R^m U {-inf}^m, u in R^m U {+inf}^m.

Rust Interface Documentation

Solver Documentation

lib.rs:

<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.2/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>

The OSQP (Operator Splitting Quadratic Program) solver is a numerical optimization package for solving convex quadratic programs in the form

\[\begin{split}\begin{array}{ll} \mbox{minimize} & \frac{1}{2} x^T P x + q^T x \\ \mbox{subject to} & l \leq A x \leq u \end{array}\end{split}\]

where \(x\) is the optimization variable and \(P \in \mathbf{S}^{n}_{+}\) a positive semidefinite matrix.

Further information about the solver is available at osqp.org.

Example

Consider the following QP

\[\begin{split}\begin{array}{ll} \mbox{minimize} & \frac{1}{2} x^T \begin{bmatrix}4 & 1\\ 1 & 2 \end{bmatrix} x + \begin{bmatrix}1 \\ 1\end{bmatrix}^T x \\ \mbox{subject to} & \begin{bmatrix}1 \\ 0 \\ 0\end{bmatrix} \leq \begin{bmatrix} 1 & 1\\ 1 & 0\\ 0 & 1\end{bmatrix} x \leq \begin{bmatrix}1 \\ 0.7 \\ 0.7\end{bmatrix} \end{array}\end{split}\] 
use osqp_rust::{CscMatrix, Problem, Settings};

// Define problem data
let P = &[[4.0, 1.0],
          [1.0, 2.0]];
let q = &[1.0, 1.0];
let A = &[[1.0, 1.0],
          [1.0, 0.0],
          [0.0, 1.0]];
let l = &[1.0, 0.0, 0.0];
let u = &[1.0, 0.7, 0.7];

// Extract the upper triangular elements of `P`
let P = CscMatrix::from(P).into_upper_tri();

// Disable verbose output
let settings = Settings::default()
    .verbose(false);

// Create an OSQP problem
let mut prob = Problem::new(P, q, A, l, u, &settings).expect("failed to setup problem");

// Solve problem
let result = prob.solve();

// Print the solution
println!("{:?}", result.x().expect("failed to solve problem"));
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Dependencies