Math Programming Incidence Graph Analysis. Tools for constructing and analyzing the incidence graph or matrix of variables and constraints in a JuMP model.
These tools can be used to detect whether and (approximately) why the Jacobian of equality constraints is structurally or numerically singular, which commonly happens as the result of a modeling error. See the documentation for more information and examples.
MathProgIncidence is registered on the Julia general package registry. It can be installed with:
julia> ]
(@v1.X) pkg> add MathProgIncidenceThis package depends on JuMP, Graphs.jl, and the dependencies thereof.
using JuMP
import MathProgIncidence
m = Model()
comps = [1, 2, 3]
@variable(m, x[comps], start=1/3.0)
@variable(m, flow_comp[comps], start=10.0)
@variable(m, flow, start=30.0)
@variable(m, rho, start=1.0)
@constraint(m, sum_comp_eqn, sum(x) == 1)
@constraint(m, comp_dens_eqn, x*rho .== [1.0, 1.1, 1.2])
@NLconstraint(m, bulk_dens_eqn, 1/rho - sum(1/x[j] for j in comps) == 0)
@constraint(m, comp_flow_eqn, x.*flow .== flow_comp)
igraph = MathProgIncidence.IncidenceGraphInterface(m)
con_dmp, var_dmp = MathProgIncidence.dulmage_mendelsohn(igraph)
oc_con = [con_dmp.overconstrained..., con_dmp.unmatched...]
oc_var = var_dmp.overconstrained
uc_con = con_dmp.underconstrained
uc_var = [var_dmp.unmatched..., var_dmp.underconstrained...]
println("Overconstrained subsystem")
println("-------------------------")
println("Constraints")
for con in oc_con
println(" $con")
end
println("Variables")
for var in oc_var
println(" $var")
end
println()
println("Underconstrained subsystem")
println("--------------------------")
println("Constraints")
for con in uc_con
println(" $con")
end
println("Variables")
for var in uc_var
println(" $var")
endMathProgIncidence.jl is open-source software released under the 3-clause BSD license. See LICENSE.md for more information.
If you use MathProgIncidence.jl in your research, we would appreciate you citing the following paper:
@article{parker2023dulmage,
title = {Applications of the {Dulmage-Mendelsohn} decomposition for debugging nonlinear optimization problems},
journal = {Computers \& Chemical Engineering},
volume = {178},
pages = {108383},
year = {2023},
issn = {0098-1354},
doi = {https://doi.org/10.1016/j.compchemeng.2023.108383},
url = {https://www.sciencedirect.com/science/article/pii/S0098135423002533},
author = {Robert B. Parker and Bethany L. Nicholson and John D. Siirola and Lorenz T. Biegler},
}