diff --git a/docs/src/optimization.md b/docs/src/optimization.md index 061b9006..b3458931 100644 --- a/docs/src/optimization.md +++ b/docs/src/optimization.md @@ -126,3 +126,65 @@ m = Model() poly = polyhedron(m, CDDLib.Library(:exact)) ``` + +## Using a Polyhedra Optimizer with MathOptInterface + +Polyhedra Optimizers by dafault support only a few constraint types in MathOptInterface (MOI). +Apply `MOI.Bridges.full_bridge_optimizer` to a Polyhedra Optimizer to enable a broader set of constraint types, such as `VectorAffineFunction`: +see the [list](http://www.juliaopt.org/MathOptInterface.jl/dev/apimanual/#Constraints-by-function-set-pairs-1) from MOI. + +As an exmaple, consider the linear program: + +```math +\[ +\max\ c x \quad \text{s.t.}\ A x \leq b +\] +``` + +where + +```julia +A = [1 1; -1 0; 0 -1] +b = [1, 0, 0] +c = [1, 0] +``` + +Let us solve this program with `CDDLib.Optimizer` in exact arithmetic. +To set up: + +```julia +using CDDLib +using MathOptInterface +const MOI = MathOptInterface + +m, n = size(A) +T = Rational{BigInt} + +# Enable `VectorAffineTerm` and `Nonpositives` +optimizer = MOI.Bridges.full_bridge_optimizer(CDDLib.Optimizer{T}(), T) + +x = MOI.add_variables(optimizer, n) +MOI.set(optimizer, MOI.ObjectiveFunction{MOI.ScalarAffineFunction{T}}(), + MOI.ScalarAffineFunction{T}(MOI.ScalarAffineTerm{T}.(c, x), 0)) +MOI.set(optimizer, MOI.ObjectiveSense(), MOI.MAX_SENSE) + +terms = MOI.VectorAffineTerm{T}.( + 1:m, MOI.ScalarAffineTerm{T}.(A, reshape(x, 1, n)) +) +f = MOI.VectorAffineFunction{T}(vec(terms), -b) +MOI.add_constraint(optimizer, f, MOI.Nonpositives(m)) +``` + +To solve: + +```julia +MOI.optimize!(optimizer) +MOI.get(optimizer, MOI.VariablePrimal(), x) +``` + +``` +2-element Array{Rational{BigInt},1}: + 1//1 + 0//1 +``` +