MathOptChordalDecomposition.jl

MathOptChordalDecomposition.jl is a MathOptInterface.jl layer that implements chordal decomposition of sparse semidefinite constraints.

Getting help

If you need help, please ask a question on the JuMP community forum.

If you have a reproducible example of a bug, please open a GitHub issue.

License

MathOptChordalDecomposition.jl is licensed under the MIT License.

Installation

Install MathOptChordalDecomposition as follows:

import PkgPkg.add("MathOptChordalDecomposition")

Use with JuMP

To use MathOptChordalDecomposition with JuMP, use MathOptChordalDecomposition.Optimizer:

using JuMP, MathOptChordalDecomposition, SCSmodel = Model(() -> MathOptChordalDecomposition.Optimizer(SCS.Optimizer))

Change SCS for any other conic solver that supports semidefinite constraints.

Basic Usage

The sdplib directory contains four semidefinite programming problems from the SDPLIB library.

The function main, defined below, reads one of the problems and constructs a JuMP.jl model.

For this example, it is significantly faster to solve the problem with MathOptChordalDecomposition than to use SCS by itself:

julia> using FileIO, JLD2, JuMP, LinearAlgebra, SCSjulia> import MathOptChordalDecomposition as MOCDjulia> function main(optimizer, name::String)           data = FileIO.load("./sdplib/$name.jld2");           F, c, m, n = data["F"], data["c"], data["m"], data["n"]               model = Model(optimizer)           set_silent(model)           @variable(model, x[1:m])           @objective(model, Min, c' * x)           @constraint(               model,               con,               LinearAlgebra.Symmetric(-F[1] + x' * F[2:end]) in PSDCone(),           )           optimize!(model)           return objective_value(model)       endmain (generic function with 1 method)julia> @time main(SCS.Optimizer, "mcp124-1")  9.447474 seconds (154.70 k allocations: 12.313 MiB)141.96561765120785julia> @time main(() -> MOCD.Optimizer(SCS.Optimizer), "mcp124-1")  0.245992 seconds (170.72 k allocations: 15.103 MiB, 1.85% compilation time)141.9887372030578