MatrixOptInterface.jl

This package is this in early development, feedback is welcome!

An interface for optimization problems in matrix forms. Several matrix forms are represented in subtypes of MathOptInterface (MOI) models. As they implement the MOI API, they can be copied directly to an MOI or JuMP model.

Here is a simple example copying a linear program represented in its standard form into JuMP:

import MatrixOptInterface
const MatOI = MatrixOptInterface
lp = MatOI.LPStandardForm{Float64, Matrix{Float64}}(MOI.MAX_SENSE, [1.0, 0.0], [1.0 1.0], [1.0])

using JuMP
model = Model()
MOI.copy_to(model, lp)

Giving some arbitrary names to the variables for pretty printing:

set_name.(all_variables(model), "x" .* string.(1:2))
print(model)

we get the following output:

Max x1
Subject to
 x1 + x2 = 1.0
 [x1, x2] ∈ MathOptInterface.Nonnegatives(2)

The LP standard form is the the only one implemented in this package. The 4 different available forms of linear programs are given below. In each form, sense is a MOI.OptimizationSense so its values are either MOI.FEASIBILITY_SENSE, MOI.MAX_SENSE or MOI.MIN_SENSE.

An LP standard form with LPStandardForm(sense, c, A, b):

sense ⟨c, x⟩
s.t.
Ax == b
 x >= 0

An LP geometric form with LPGeometricForm(sense, c, A, b):

sense ⟨c, x⟩
s.t.
Ax <= b

A generic LP form with LPForm(sense, c, A, c_lb, c_ub, v_lb, v_ub):

sense ⟨c, x⟩
s.t.
c_lb <= Ax <= c_ub
v_lb <=  x <= v_ub

An LP Solver form with LPSolverForm(sense, c, A, b, senses, v_lb, v_ub):

sense ⟨c, x⟩
s.t.
Ax senses b
v_lb <=  x <= v_ub

where senses is a vector whose ith entry is either

• MatOI.EQUAL_TO if (Ax)_i = b_i,
• MatOI.LESS_THAN if (Ax)_i <= b_i,
• MatOI.GREATER_THAN if (Ax)_i >= b_i.

Transition from linprog

If you are used to MathProgBase's, MATLAB's or scipy's linprog function, this package provides an easy transition. The package does not provide a one-shot function that takes the form as input are returns the solution and status as in general, solvers may have multiple solutions to report and the status cannot be summarized in a single value. MathOptInterface embraces this complexity and allows to retrieve multiple solutions, has 4 different solver-independent statuses (MOI.TerminationStatus, MOI.PrimalStatus, MOI.DualStatus and MOI.RawStatusString) and also allows solvers to provide solver independent statuses. For these reasons, there is no linprog functions covering all use cases but using this packages one covering your use cases can be implemented in just a few lines:

1. Create the appropriate structure from the matrix data, e.g. LPForm, LPSolverForm, ...
2. Copy it to a JuMP model or MOI optimizer.
3. Call JuMP.optimize! or MOI.optimize!.
4. Retrieve and return solutions and statuses.