Support QP interface via MOI #30

mtanneau · 2026-01-10T20:21:02Z

This PR introduces support for solving Quadratic Programs with cuOpt.

Notes:

cuOpt only supports QPs with convex objectives. The MOI wrapper does not perform any convexity checks, it passes the matrix as-is to the solver
while building the wrapper, I encountered an upstream bug (see [BUG] cuOpt crashes when solving QP with no linear constraints NVIDIA/cuopt#759) that led me to disable two MOI tests
I have tested this locally on a DGX Spark machine as follows:
- OS: Ubuntu (Linux aarch64)
- GPU: GB10
- cuOpt: v25.12.0

Please see extra comments in the diff

Project.toml

src/MOI_wrapper.jl

mtanneau · 2026-01-10T20:24:22Z

src/MOI_wrapper.jl

+    # Is this a QP or an LP?
+    has_quadratic_objective = length(qobj_matrix_values) > 0
+    if has_quadratic_objective && has_integrality
+        error("cuOpt does not support models with quadratic objectives _and_ integer variables")


Not sure what the best error / error message is here, happy to modify this as requested.

Note that cuOpt does not support MIQPs, only MILP or continuous QP

This error is okay for now.

As other options: you could remove the error and make it so that TerminationStatus was MOI.INVALID_MODEL. Or you could throw(MOI.SetAttributeNotAllowed(obj_attr, "cuOpt does not support ...")) but it's a coin toss whether the objective or integer constraint is the problem. And MOI doesn't have a bridge to fix this so the error is going to propagate to the user anyway.

src/MOI_wrapper.jl

mlubin · 2026-01-11T01:45:37Z

From the README:

Note: This version of cuOpt.jl supports the Nvidia cuOpt 25.08, 25.10, and 25.12 releases.

Which version of cuOpt introduced this QP API?

mtanneau · 2026-01-11T03:46:39Z

Which version of cuOpt introduced this QP API?

It was added to the C API in cuOpt v25.12 (See release notes)

mlubin · 2026-01-11T17:23:33Z

@rgsl888prabhu should weigh in on if we want to bump the minimum supported version of cuOpt to 25.12 or add appropriate error messages when users try to solve QPs with an older version. Bumping the required version is ok with me since it makes maintenance of the wrapper easier.

src/MOI_wrapper.jl

blegat · 2026-01-12T07:40:19Z

I think DCO is failing because the commit made via the github UI were not signed off

Signed-off-by: mtanneau <[email protected]>

mtanneau · 2026-01-12T14:54:45Z

I think DCO is failing because the commit made via the github UI were not signed off

Thank you, fixed and rebased

rg20

Thank you for implementing the QP interface for cuOpt!

I think the cuOpt version support might need changes in cuOpt.jl file. The QP support only works from 25.12.

rg20 · 2026-01-12T13:58:18Z

src/MOI_wrapper.jl

+        v = qterm.coefficient
+        if i == j
+            # Adjust diagonal coefficients to match cuOpt convention
+            v /= 2


Not sure if this is accurate.

cuOpt expects users to provide the true objective function.

For example: if you are minimizing x1^2 + x2^2, the matrix should be [1 0; 0 1], cuOpt internally minimizes for (1/2) [x1 x2] [2 0; 0 2] [x1; x2] in this case.

cuOpt expects users to provide the true objective function.

https://www.youtube.com/watch?v=M31xoZGyj9w&t=2698s

What happens to the off-diagonal terms?

cuOpt is not necessarily expecting the matrix to be symmetric.

If the objective is xT Q x + cT x, we internally symmetrize and solve for (1/2) xT (Q + QT) x + cT x

So if the objective is x1^2 + x2^2 + 2 x1 x2,

Q can be: [1 2; 0 1], or [1 0; 2 1] or [1 1; 1; 1]

(including the links for completeness)

cuOpt docs: https://docs.nvidia.com/cuopt/user-guide/latest/lp-qp-features.html#quadratic-programming

MOI docs: https://jump.dev/MathOptInterface.jl/stable/reference/standard_form/#MathOptInterface.ScalarQuadraticFunction

I believe the /2 factor for diagonal terms is required for correctness, but agreed it's not super clear why at first.

The current MOI wrapper uses a JuMP-level data structure to store the optimization model as the user builds it. That internal representation abides by MOI conventions.

when optimize! gets called, the problem data is flushed from the JuMP-level data store into a cuOpt-level data structure --> this is why this PR mostly modifies the copy_to function.

Hence, when we access the quadratic objective in copy_to, we get as input an MOI.ScalarQuadraticFunction, which abides by the MOI convention described in the docs above.

Here is a small example to illustrate this

using JuMP model = Model() @variable(model, x) @variable(model, y) @objective(model, Min, x*x + 2*x*y + 3*y*y) objective_function(model) # x² + 2 x*y + 3 y² # Now, access the MOI representation F = MOI.get(model, MOI.ObjectiveFunctionType()) f = MOI.get(model, MOI.ObjectiveFunction{F}()) f.quadratic terms

the last line outputs

3-element Vector{MathOptInterface.ScalarQuadraticTerm{Float64}}: MathOptInterface.ScalarQuadraticTerm{Float64}(2.0, MOI.VariableIndex(1), MOI.VariableIndex(1)) MathOptInterface.ScalarQuadraticTerm{Float64}(2.0, MOI.VariableIndex(1), MOI.VariableIndex(2)) MathOptInterface.ScalarQuadraticTerm{Float64}(6.0, MOI.VariableIndex(2), MOI.VariableIndex(2))

--> you can see that the diagonal coefficients were multiplied by 2. This was done by MOI in accordance with its convention.

@rg20 I can add the following:

add link to the MOI docs on quadratic function in that comment, to provide additional context

add a couple of unit tests to validate the cuOpt solution and objective value when solving QP from MOI

My conclusion with this all is that the only valid way is to test, test, test, test, and test. There are too many subtleties to try and logically reason about the transformations, and every time I do, I end up making a mistake.

There are tests in MOI for various cases, but these are precisely the ones that you're skipping because of the upstream bug... 😢 ("test_objective_qp_ObjectiveFunction_zero_ofdiag" and "test_objective_qp_ObjectiveFunction_edge_cases").

@mtanneau thanks for explaining the subtleties in the MOI wrapper.

Added more unit tests that specifically trigger the QP objective.
Notes:

the upstream issue regarding QP with no constraints might get fixed in cuopt v26.02 (tracking Use augmented system when there are no constraints NVIDIA/cuopt#765), which would allow to run more MOI-level tests.

if the team is OK with adding JuMP as a test dependency, I'm happy to add similar tests where the QP is built from JuMP, not from MOI.

JuMP shouldn't be a test dependency; MOI-style tests should be sufficient

rgsl888prabhu · 2026-01-12T20:29:05Z

@rgsl888prabhu should weigh in on if we want to bump the minimum supported version of cuOpt to 25.12 or add appropriate error messages when users try to solve QPs with an older version. Bumping the required version is ok with me since it makes maintenance of the wrapper easier.

@mlubin Yes, lets bump it to 25.12.

Signed-off-by: mtanneau <[email protected]>

mtanneau commented Jan 10, 2026

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mtanneau force-pushed the qp-interface-moi branch from 64e7474 to 3a13f8c Compare January 10, 2026 22:41

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mtanneau added 6 commits January 12, 2026 09:52

Support QP interface via MOI

a926678

Signed-off-by: mtanneau <[email protected]>

Move objective data extraction to separate method

bbcb4f4

Signed-off-by: mtanneau <[email protected]>

Format

ace38fd

Signed-off-by: mtanneau <[email protected]>

Fix typos

a7ff4a2

Signed-off-by: mtanneau <[email protected]>

In-place offset + remove comments

7c6a48a

Signed-off-by: mtanneau <[email protected]>

Move import

067d973

Signed-off-by: mtanneau <[email protected]>

mtanneau force-pushed the qp-interface-moi branch from c1313e4 to 067d973 Compare January 12, 2026 14:52

rg20 reviewed Jan 12, 2026

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mtanneau added 4 commits January 12, 2026 16:28

Bump cuopt compat version to 25.12

1841980

Signed-off-by: mtanneau <[email protected]>

Explain MOI vs cuOpt convention re:quadratic functions

c108151

Signed-off-by: mtanneau <[email protected]>

Add QP unit tests

b27e7d0

Signed-off-by: mtanneau <[email protected]>

Fix typos + format

2ee820d

Signed-off-by: mtanneau <[email protected]>

Support QP interface via MOI #30

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Support QP interface via MOI #30

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