A fast, reliable, and open-source convex cone solver.
SCS (Splitting Conic Solver) is a numerical optimization package for solving large-scale convex quadratic cone problems. The code is freely available on GitHub. It solves primal-dual problems of the form
over variables
\(x \in \mathbf{R}^n\) |
primal variable |
\(y \in \mathbf{R}^m\) |
dual variable |
\(s \in \mathbf{R}^m\) |
slack variable |
with data
\(A \in \mathbf{R}^{m \times n}\) |
sparse data matrix, see Data matrices |
\(P \in \mathbf{S}_+^{n}\) |
sparse, symmetric positive semidefinite matrix |
\(c \in \mathbf{R}^n\) |
dense primal cost vector |
\(b \in \mathbf{R}^m\) |
dense dual cost vector |
\(\mathcal{K} \subseteq \mathbf{R}^m\) |
nonempty, closed, convex cone, see Cones |
\(\mathcal{K}^* \subseteq \mathbf{R}^m\) |
dual cone to \(\mathcal{K}\) |
At termination SCS will either return points \((x^\star,y^\star,s^\star)\) that satisfies the optimality conditions to the desired accuracy, or a certificate of primal or dual infeasibility to the designated infeasibility accuracy.
Features
Efficient: Designed to scale to large problems.
Flexible: Supports quadratic objectives and a large range of cones.
Free and open source: Distributed under the permissive MIT license.
Detects infeasibility: Robustly and reliably detects infeasible problems.
Interfaces: Bindings for many languages, including C, Python, Julia, R, MATLAB, and Ruby.
Warm starts: Easily warm-started, and the matrix factorization can be cached.
Matrix-free: Optionally use an indirect linear system solver, or a GPU version.
Supported: A supported solver in CVX, CVXPY, YALMIP, Convex.jl and JuMP.
Accelerated: Includes acceleration that can improve convergence to high accuracy.
Battle-tested: The first ADMM-based solver available, and in wide usage.
Development
SCS is a community project, built from the contributions of many researchers and engineers. The primary maintainer is Brendan O’Donoghue. We appreciate all contributions. To get involved, see our contributing guide.