OSQP does not detect the Objective Function while reading nl file model through MathOptInterface

[Eyantra698Sumanto]

Description

OSQP does not detect the Objective Function while reading nl file through MathOptInterface.

We tried running a simple problem to demonstrate the issue:

$$min ( x^2 +y^2)$$ $$s. t. \ \ x>=1, y>=1$$

Using the following approaches:

1. OSQP directly using JuMP by defining the model in Julia
2. OSQP using the MathOptInterface to read the model from .nl file

The 1st one works fine and gives the correct results while the 2nd one doesn't detect the Objective Function correctly.

Steps to Reproduce

Extract the zip file attached here:
circle.zip

1. Run the circle_osqp.jl using julia circle_osqp.jl. This runs OSQP directly using JuMP by defining the model in Julia.
2. Run the circle_osqp_nl.jl using julia circle_osqp_nl.jl. This runs OSQP using the MathOptInterface to read the model from .nl file.

Expected Behavior

Both circle_osqp.jl and circle_osqp_nl.jl must give the same the same result. But, the objective is not getting detected in case of circle_osqp_nl.jl due to which the objective value in the result is 0.

Version and OS

• julia-1.7.0
• OS: Debian GNU/Linux 11 (bullseye)

[goulart-paul]

Did you mean to include a sample .nl file? There is nothing to load for the second script.

[goulart-paul]

Never mind, I was able to reproduce it.

The problem is that the .nl file format produces a model with a general nonlinear objective, and OSQP only knows what to do with quadratic or affine objectives. This should have resulted in an error, but was instead the model was accepted and the objective function not correctly populated.

Fix is here: osqp/OSQP.jl#128

Note that that the "fix" is to just crash with a warning that a nonlinear model is not suitable for the solver. I think you would be better served with a different file format if you want to use this solver.

[Eyantra698Sumanto]

Hi @goulart-paul , thanks a lot for your reply! Can you please provide me with a simple example file which can be correctly read using the MOI and solved with OSQP then? I tried some instances from QPLIB but those are not working well. Please help me with this.

[goulart-paul]

I would try just round tripping a test problem through the various support JuMP file formats. Here's an example showing that mps format works for your toy problem:

using JuMP, OSQP

format = MOI.FileFormats.FORMAT_MPS

# Define the model
model1 = Model(OSQP.Optimizer)

# Define variables
@variable(model1, x >= 1)
@variable(model1, y >= 1)

# Define the objective function: x^2 + y^2 + 2
@objective(model1, Min, x^2 + y^2 + 2)

# Solve the problem
optimize!(model1)

# save and reload 
JuMP.write_to_file(model1,"example.txt", format = format)
model2 = JuMP.read_from_file("example.txt", format = format)

set_optimizer(model2, OSQP.Optimizer)
optimize!(model2)

@assert objective_value(model1) == objective_value(model2)