Exact hull reformulation for quadratic constraints

[sergey-gusev94]

Fixes # .

Summary/Motivation:

This PR adds support for the exact hull reformulation for quadratic constraints in Generalized Disjunctive Programming (GDP).

The current gdp.hull transformation applies perspective-function based relaxations for nonlinear constraints. While effective for many nonlinear expressions, this approach can produce weaker relaxations for quadratically constrained disjunctions.

This PR implements the exact hull reformulation for quadratic constraints described in:

Gusev, S., & Bernal Neira, D. E. (2025).
Exact Hull Reformulation for Quadratically Constrained Generalized Disjunctive Programs.
https://arxiv.org/abs/2508.16093

The implementation extends the existing hull transformation with an optional configuration flag (which is False by default) that detects quadratic constraints and applies the exact hull formulation when appropriate.

For convex quadratic constraints, the reformulation is expressed as a rotated second-order cone (SOC) representable constraint. For nonconvex quadratics and equality constraints, the general exact hull formulation is used.

Convexity is determined automatically through eigenvalue analysis of the Hessian matrix.

This provides a tighter relaxation for quadratic GDP models and maintains the quadratic structure of constraints in hull reformulation.

Changes proposed in this PR:

• Extend the gdp.hull transformation with a new configuration option:

  • exact_hull_quadratic (default: False)

• When enabled, quadratic constraints inside disjuncts are reformulated using the exact hull formulation instead of the standard perspective function.

• Implement automatic convexity detection via eigenvalue decomposition of the quadratic Hessian matrix.

• Apply different reformulations depending on structure:

  • Convex quadratic inequalities
    Reformulated using a rotated second-order cone representation.

  • Nonconvex quadratics or equalities
    Reformulated using the general exact hull formulation.

• Add a configuration parameter:

  • eigenvalue_tolerance
    Controls numerical tolerance when checking positive or negative semidefiniteness of the Hessian.

• Extend the implementation in pyomo.gdp.plugins.hull to support these reformulations.

• Add unit tests verifying:

  • correctness of the generated constraints
  • compatibility with existing hull behavior
  • correctness of variable disaggregation and mappings.

The default behavior of gdp.hull is unchanged unless the new option is enabled.

Example usage:

TransformationFactory("gdp.hull").apply_to(
    model,
    exact_hull_quadratic=True
)

Legal Acknowledgement

By contributing to this software project, I have read the contribution guide and agree to the following terms and conditions for my contribution:

1. I agree my contributions are submitted under the BSD license.
2. I represent I am authorized to make the contributions and grant the license. If my employer has rights to intellectual property that includes these contributions, I represent that I have received permission to make contributions and grant the required license on behalf of that employer.

[codecov]

Codecov Report

❌ Patch coverage is 96.61017% with 6 lines in your changes missing coverage. Please review.
✅ Project coverage is 89.78%. Comparing base (ae0ae63) to head (86bfc81).
⚠️ Report is 119 commits behind head on main.

Files with missing lines	Patch %	Lines
pyomo/gdp/plugins/hull.py	96.61%	6 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3874      +/-   ##
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+ Coverage   86.80%   89.78%   +2.97%     
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  Files         903      903              
  Lines      106604   106780     +176     
==========================================
+ Hits        92537    95871    +3334     
+ Misses      14067    10909    -3158     

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default	86.30% <96.61%> (?)
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[emma58]

This looks pretty good, but I'm submitting a partial review because there's one major revision: See my notes below, but can you please rewrite this to use the QuadraticRepnVisitor rather than generate_standard_repn? You'll be able to get all the same data, though it will come in a slightly different structure. But it is much more robust to edge cases--I think generate_standard_repn is not long for this world, actually.

[emma58]

Thanks for the docstring!!

[mrmundt]

@jsiirola , @blnicho - This one is ready for a re-review!

[emma58]

Thank you so much for making the change to the QuadraticRepnVisitor! This is looking quite good. Most of the changes suggested below are fairly minor, though if you can, it would be nice to abandon generate_standard_repn in the tests as well and to add public APIs where you are testing private components added by the transformation.

[emma58]

I would recommend against testing that depends on private names since any naming changes will break tests. It might be worth including an API (using the private_data Block) to retrieve the auxiliary variables, and then you can test them that way.

[sergey-gusev94]

Addressed in 73e309e

[emma58]

Thank you for the lightning-fast response! A couple more minor comments and then I really will be done complaining!