Introduction

ConicSolve.jl is a Primal-Dual Interior-Point method constrained optimization solver based on the paper Vandenberghe, 2010, The CVXOPT linear and quadratic cone program solvers. It can be used to solve several problem classes including LP (Linear Program), QP (Quadratic Program) and SDP (Semidefinite Program).

The solver requires that problems be expressed as a cone quadratic program (cone QP) i.e. in the form

\[\begin{aligned} \text{minimize}\qquad & (1/2)x^TPx + c^Tx \\ \text{subject to}\qquad & Gx + s = h \\ & Ax = b \\ & s \succeq 0 \end{aligned}\]

where $P$ is a PSD (positive semidefinite) matrix, $s$ is a generalized inequality with respect to a self-dual convex cone.

Installation

To use ConicSolve.jl, install Julia, then at the Julia REPL, type:

using Pkg
Pkg.add("ConicSolve")
using ConicSolve

GPU Acceleration

ConicSolve.jl uses CUDA.jl to accelerate matrix factorization methods for solving the KKT equations. Refer to CUDA.jl for additional installation requirements.

Note:
GPU Acceleration from running ConicSolve.jl as a standalone binary executable is currently not supported.

Enable GPU acceleration via the following code snippet

using CUDA
using ConicSolve

Ensure the solver property solver.device = GPU has been set.

How to use

There are two ways to construct an optimization problem in ConicSolve.jl

1. Using the Low Level API
2. Using models to precompute matrices before invoking the low level API

Using the Low Level API

julia> using ConicSolve
julia> p_1 = 16 # for example, 16 x 16 SDP matrix
julia> p_2 = 136 # for example, 136 elements (or 16 * 17 / 2) in lower triangular SDP matrix
julia> A = [] # problem specific, replace with your values
julia> G = [] # problem specific, replace with your values
julia> P = [] # problem specific, replace with your values
julia> b = [] # problem specific, replace with your values
julia> c = [] # problem specific, replace with your values
julia> h = [] # problem specific, replace with your values
julia> cones::Vector{Cone} = []
julia> push!(cones, PSDCone(p_1))
julia> push!(cones, NonNegativeOrthant(p_2))
julia> cone_qp = ConeQP(A, G, P, b, c, h, cones)
julia> solver = Solver(cone_qp)
julia> run_solver(solver)

Using an SDP Model

julia> using ConicSolve
julia> data = [] # your data here
julia> mask = [] # your data here
julia> sdp = SDP(data)
julia> set_values(sdp, mask)
julia> set_nonnegative_constraint(sdp)
julia> c = get_trace(sdp)
julia> set_objective(sdp, c)
julia> qp = get_qp(sdp)
julia> solver = Solver(qp)
julia> run_solver(solver)

Examples

In the examples directory you will find several examples which gives an idea of how to use the API for this solver.

How to cite

@misc{Leong2025,
    title = {ConicSolve: A constrained optimization solver for scientific advancement},
    author = {Alexander Leong},
    url = {https://github.com/alexander-leong/ConicSolve.jl}
}

Contributions

This solver has been developed for the sole purpose of investigating new and existing applications for Interior Point based methods by creating a solver that has minimal project dependencies, is highly performant, general purpose, extensible and most importantly is free for public use.

This project is still a work in progress. Any contributions to add additional examples and use cases are welcome! Even if you can't contribute, please consider providing financial assistance if you have found this project useful in your work.

Reference Material

License

MIT License

Copyright (c) 2025 Alexander Leong

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.