second order cone constraint in JuMP 0.19 with gurobi solver

nitu0317 · March 13, 2019, 8:42am

I failed to add SOCP constraint to my model with gurobi solver after updating JuMP to 0.19.

Since norm is no longer supported, I tried the example provided in documentation,

using JuMP,Gurobi,MathOptInterface

env = Gurobi.Env()

model = Model(with_optimizer(Gurobi.Optimizer, env))

@variable(model, x)

@variable(model, t)

#@constraint(model, norm([x-1, x-2]) <= t)

@constraint(model, [t, x-1, x-2] in SecondOrderCone())

print(model)

JuMP.optimize!(model)

But the error message says

ERROR: LoadError: Constraints of type MathOptInterface.VectorAffineFunction{Float64}-in-MathOptIInterface.SecondOrderCone are not supported by the solver and there are no bridges that can refrormulate it into supported constraints.

Please help on this.

blegat · March 13, 2019, 12:00pm

For Gurobi you need to enter it as a quadratic constraint. The transformation from SOC to quadratic is currently discussed here:

github.com/jump-dev/MathOptInterface.jl

Add SOCtoQuad bridge

jump-dev:master ← jump-dev:bl/soctoquad

opened 08:57PM - 19 Aug 18 UTC

blegat

+152 -38

Adds a SOCtoQuad bridges which allows to use the ```julia @constraint(model, […t, x, y] in SecondOrderCone()) ``` with solvers expecting SOC constraint in quadratic form (e.g. [LQOI](https://github.com/JuliaOpt/LinQuadOptInterface.jl) solvers). It also add missing methods in MOIU for quadratic functions. While doing this, I noticed, that the `_pair` and `_canonicalize` functions of `src/functions.jl` were doing the same thing than `MOIU.termindices` and `MOIU.coefficient`. Hence I moved `coefficient` and `termindices` (rename `term_indices` following the style guide) to MOI and renamed and documented `_pair` into `term_pair`. I also noticed that we have both `MOI._constant` and `MOIU._constant` hence I have removed `MOIU._constant`. We should still replace this by a function with a better name and doc but this will not be addressed in this PR. Closes https://github.com/JuliaOpt/MathOptInterfaceBridges.jl/issues/92

We try to make a decision about this during this afternoon collaboration time at JuMP-dev.

anubhavratha · August 30, 2019, 3:26pm

Hi, new to Julia and JuMP here, but really enjoying it so far.

Unfortunately, I am a bit stuck with this issue and would be happy to know how the dev plan for SOCtoQuadBridge look like at the moment?

As I try to convert an old (but working fine) Python code to Julia, I run into the issue that Gurobi in JuMP cannot automatically reformulate constraints of form x^2 + y^2 <= z^2, z >= 0 (“Q-matrix” is not PSD but has only 1 negative eigenvalue, so I believe this constraint should be SOC representable). It throws the error that “Q-matrix is not PSD”.The equivalent constraint in the GurobiPy API does result in an “optimal” solution.

A minimal example is posted below. For my larger problem, unfortunately, MOSEK with the SecondOrderCone() constraint is not working well as Mosek solver stalls (JuMP status: SLOW_PROGRESS, Mosek status: Mosek.MSK_RES_TRM_STALL).

It is possible that I am doing something wrong.
Many thanks in advance for your help.

using JuMP, Mosek, MosekTools, Gurobi

#Uncomment for Gurobi
m = Model(with_optimizer(Gurobi.Optimizer, Presolve=0, OutputFlag=1, DualReductions=0))

#Uncomment for Mosek
#m = Model(with_optimizer(Mosek.Optimizer,MSK_IPAR_LOG=1,MSK_DPAR_INTPNT_CO_TOL_REL_GAP=1.0e-10))

@variable(m, x)
@variable(m, y)
@variable(m, z)

@constraint(m, z >= 0)
@constraint(m, 1 <= x <= 3)
@constraint(m, 1 <= y <= 3)

#Uncomment for Gurobi
@constraint(m, x*x + y*y <= z*z)

#Uncomment for Mosek
#@constraint(m, [z,x,y] in SecondOrderCone())


@objective(m, Min, x+y)

optimize!(m)
status = termination_status(m)

println(status)
println(JuMP.value(x))
println(JuMP.value(y))
println(JuMP.value(z))

odow · August 30, 2019, 6:27pm

You should use bounds instead of constraints.

@variable(m, 1 <= x <= 3)
@variable(m, 1 <= y <= 3)
@variable(m, z >= 0)

Gurobi can’t preserve your constraints to prove z >= 0 .

SecondOrderCone support is coming. See https://github.com/JuliaOpt/Gurobi.jl/pull/231

anubhavratha · August 30, 2019, 6:52pm

Thanks so much, Oscar. It works now for my larger problem too. Looking forward to and following updates on the SecondOrderCone support for Gurobi.

wenqi_kou · September 27, 2019, 5:55am

Hi Oscar, is SecondOrderCone supported by Gurobi now?
As you said " Gurobi can’t preserve constraints to prove z >= 0 ", I have a similar issue. But my constraint z >= 0 is in a loop, so I cannot use bound since I cannot attach same name variable to my model. If so, any better way to solve this problem? Thanks in advance.

odow · September 27, 2019, 1:21pm

Yes. It just needs a new tag: Bump version by odow · Pull Request #259 · jump-dev/Gurobi.jl · GitHub

For now, you could try ] add Gurobi#master.

But my constraint z >= 0 is in a loop, so I cannot use bound since I cannot attach same name variable to my model. If so, any better way to solve this problem?

You want to use the anonymous syntax:

z = @variable(model, lower_bound = 0)

See: Variables · JuMP

wenqi_kou · September 27, 2019, 1:38pm

I am sorry. I am new here. What do you mean ] add Gurobi#master here? Can you explain more? Thanks!

odow · September 27, 2019, 1:52pm

Open the Julia REPL and type

julia> ] add Gurobi#master

This will install the latest version of Gurobi.jl. E.g.,

wenqi_kou · September 27, 2019, 4:53pm

Thanks but julia return this:

and here is my Pkg.status():

What should I do?

odow · September 27, 2019, 7:14pm

Try running ] up first. You need JuMP 0.20

wenqi_kou · September 27, 2019, 8:25pm

It works now! Thank you so much, Oscar.