Compatibility with LinQuadOptInterface solvers (like Gurobi and GLPK)

[rdeits]

Currently, constrained optimization doesn't work with the upcoming Gurobi MOI interface. For example:

optimizer = Gurobi.GurobiOptimizer()
model = Model(optimizer)
x = Variable(model)
lhs = [x]
rhs = [0.]
@constraint model lhs <= rhs
solve!(model)

gives:

ArgumentError: ModelLike of type Gurobi.GurobiOptimizer does not support setting the attribute `ConstraintFunction`

Stacktrace:
 [1] hidden_set!(::Gurobi.GurobiOptimizer, ::MathOptInterface.ConstraintFunction, ::MathOptInterface.ConstraintIndex{MathOptInterface.VectorAffineFunction{Float64},MathOptInterface.Nonpositives}, ::MathOptInterface.VectorAffineFunction{Float64}) at /home/rdeits/locomotion/explorations/simple-qp-miqp/packages/v0.6/MathOptInterface/src/attributes.jl:588
 [2] update!(::SimpleQP.Constraint{Float64,MathOptInterface.Nonpositives}, ::SimpleQP.Model{Float64,Gurobi.GurobiOptimizer}) at /home/rdeits/locomotion/explorations/simple-qp-miqp/packages/v0.6/SimpleQP/src/model.jl:125
 [3] update!(::SimpleQP.Model{Float64,Gurobi.GurobiOptimizer}) at /home/rdeits/locomotion/explorations/simple-qp-miqp/packages/v0.6/SimpleQP/src/model.jl:136
 [4] solve!(::SimpleQP.Model{Float64,Gurobi.GurobiOptimizer}) at /home/rdeits/locomotion/explorations/simple-qp-miqp/packages/v0.6/SimpleQP/src/model.jl:149

(using SimpleQP master, Gurobi.jl with jump-dev/Gurobi.jl#125 , MOI master, and LQOI with JuliaOpt/LinQuadOptInterface.jl#29 ).

It looks like LInQuadOptInterface defines the available canset/canmodify methods, and it only supports things like scalar variable change rather than replacing the constraint function. Gurobi seems to have the relevant low-level APIs to change variable coefficients: https://www.gurobi.com/documentation/8.0/refman/c_grbchgcoeffs.html so I think this should at least be possible. For example, we could probably implement additional canset/set! methods in Gurobi.jl to supplement the ones implemented in LQOI. Or maybe we could update LQOI to allow setting an affine constraint function by using the available modify! methods.

[tkoolen]

Yeah, the other (non-OSQP) solver interfaces were pretty far behind, and I guess they're still not quite there. I see you already opened an issue with LQOI (JuliaOpt/LinQuadOptInterface.jl#32), which I was going to suggest.

[rdeits]

Oh, yeah, I was just about to cross-post that here 🙂

[rdeits]

JuliaOpt/LinQuadOptInterface.jl#37 allows set!(..., ::ConstraintFunction) for LQOI solvers, but I'm still running into issues with SimpleQP:

model = Model(GLPK.GLPKOptimizerLP())
x = Variable(model)
lhs = [x]
rhs = [0.]
@constraint model lhs <= rhs
solve!(model)

MethodError: no method matching passattributes!(::GLPK.GLPKOptimizerLP, ::SimpleQP.SimpleQPMOIModel{Float64}, ::Bool, ::MathOptInterface.Utilities.IndexMap, ::Array{Any,1})
Closest candidates are:
  passattributes!(::MathOptInterface.ModelLike, ::MathOptInterface.ModelLike, ::Bool, ::MathOptInterface.Utilities.IndexMap) at /home/rdeits/locomotion/explorations/linquadopt-gurobi/packages/v0.6/MathOptInterface/src/Utilities/copy.jl:39
  passattributes!(::MathOptInterface.ModelLike, ::MathOptInterface.ModelLike, ::Bool, ::MathOptInterface.Utilities.IndexMap, ::Function) at /home/rdeits/locomotion/explorations/linquadopt-gurobi/packages/v0.6/MathOptInterface/src/Utilities/copy.jl:39
  passattributes!(::MathOptInterface.ModelLike, ::MathOptInterface.ModelLike, ::Bool, ::MathOptInterface.Utilities.IndexMap, ::Function, ::Function) at /home/rdeits/locomotion/explorations/linquadopt-gurobi/packages/v0.6/MathOptInterface/src/Utilities/copy.jl:39
  ...

Stacktrace:
 [1] copyconstraints!(::GLPK.GLPKOptimizerLP, ::SimpleQP.SimpleQPMOIModel{Float64}, ::Bool, ::MathOptInterface.Utilities.IndexMap, ::Type{MathOptInterface.VectorAffineFunction{Float64}}, ::Type{MathOptInterface.Nonpositives}) at /home/rdeits/locomotion/explorations/linquadopt-gurobi/packages/v0.6/MathOptInterface/src/Utilities/copy.jl:90
 [2] defaultcopy!(::GLPK.GLPKOptimizerLP, ::SimpleQP.SimpleQPMOIModel{Float64}, ::Bool) at /home/rdeits/locomotion/explorations/linquadopt-gurobi/packages/v0.6/MathOptInterface/src/Utilities/copy.jl:125
 [3] initialize!(::SimpleQP.Model{Float64,GLPK.GLPKOptimizerLP}) at /home/rdeits/locomotion/explorations/linquadopt-gurobi/packages/v0.6/SimpleQP/src/model.jl:142
 [4] solve!(::SimpleQP.Model{Float64,GLPK.GLPKOptimizerLP}) at /home/rdeits/locomotion/explorations/linquadopt-gurobi/packages/v0.6/SimpleQP/src/model.jl:195

[rdeits]

That MethodError is jump-dev/MathOptInterface.jl#426

[rdeits]

Ok, I think I have the constraint issues worked out. Unfortunately, it looks like the way quadratic objectives are handled is different between OSQP and LQOI. Specifically, the doubling of the quadratic coefficients along the diagonal of the cost matrix results in the wrong answer being returned. For example:

using SimpleQP, Gurobi
model = Model(GurobiOptimizer())
x = [Variable(model) for _ in 1:1]
@objective model Minimize (x[1] - 1.5)^2
solve!(model)
SimpleQP.value.(model, x)

gives an optimal solution of 0.75, whereas if we undo the doubling by minimizing (0.5 * x[1] - 1.5)^2 we get 1.5. OSQPOptimizer gives 1.5 for the original model, as expected.

[tkoolen]

I think we can close this now. Currently requires master versions of MOI, LQOI, and solver packages.