added exact hull reformulations

[sergey-gusev94]

Fixes # .

Summary/Motivation:

The standard hull reformulation uses perspective functions for all nonlinear constraints, which does not exploit the structure of quadratic constraints. For quadratics, an exact hull reformulation exists that produces tighter relaxations — using conic (rotated SOC) constraints for convex quadratics and a direct disaggregated quadratic form for non-convex ones.

Changes proposed in this PR:

Added exact_hull_quadratic configuration option (default False) to Hull_Reformulation that enables exact hull treatment of quadratic constraints.
Modified _transform_constraint to detect degree-2 constraints when the flag is active and delegate to new exact hull logic instead of the standard perspective function.
Added _build_exact_quadratic_hull method that builds the symmetric Q matrix, determines convexity via eigenvalue decomposition, and dispatches to the appropriate reformulation strategy.
Added _build_general_exact_hull_expr method for non-convex/equality quadratics: constructs v'Qv + c'vy + dy**2.
Added _build_conic_exact_hull_expr method for convex quadratics: introduces auxiliary variable t >= 0, adds rotated SOC constraint v'Qv <= ty, and returns linear expression t + c'v + dy.
Added numpy, generate_standard_repn, and NonNegativeReals imports.
Existing behavior is unchanged when the flag is not set.

Legal Acknowledgement

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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.

[Copilot]

Pull request overview

This PR adds an exact_hull_quadratic configuration option to the Hull GDP reformulation in Pyomo. When enabled, quadratic constraints (polynomial degree 2) are reformulated using mathematically exact hull formulations instead of the standard perspective function approach, exploiting the structure of quadratic constraints to produce tighter relaxations.

Changes:

• Added exact_hull_quadratic config option (default False) to Hull_Reformulation and modified _transform_constraint to detect degree-2 constraints and dispatch to new exact hull logic.
• Added _build_exact_quadratic_hull method that constructs the Q matrix, determines convexity via eigenvalue decomposition, and dispatches to conic (for convex) or general (for non-convex) formulations.
• Added _build_general_exact_hull_expr and _build_conic_exact_hull_expr helper methods implementing the two reformulation strategies, plus new imports for numpy, generate_standard_repn, and NonNegativeReals.

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[Copilot]

@sergey-gusev94 I've opened a new pull request, #3, to work on those changes. Once the pull request is ready, I'll request review from you.

[Copilot]

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Copilot reviewed 1 out of 1 changed files in this pull request and generated 4 comments.

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[Copilot]

@sergey-gusev94 I've opened a new pull request, #4, to work on those changes. Once the pull request is ready, I'll request review from you.

[Copilot]

@sergey-gusev94 I've opened a new pull request, #5, to work on those changes. Once the pull request is ready, I'll request review from you.

[Copilot]

@sergey-gusev94 I've opened a new pull request, #6, to work on those changes. Once the pull request is ready, I'll request review from you.

[Copilot]

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Copilot reviewed 3 out of 3 changed files in this pull request and generated no new comments.

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[bernalde]

I left a few small comments that should be easy to address.
As a general comment, allow for tests to be executed in your fork through Github actions, as currently I'm unsure whether this would pass tests from pyomo (including linting, and coverage).
There also seems to be some missing changes from copilot so address them locally rather than waiting for copilot to finish those

[Copilot]

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[Copilot]

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Copilot reviewed 3 out of 3 changed files in this pull request and generated 1 comment.

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[bernalde]

This issue is breaking some tests:

> /home/runner/work/pyomo/pyomo/pyomo/gdp/plugins/hull.py:121: SyntaxWarning: "\l" is an invalid escape sequence. Such sequences will not work in the future. Did you mean "\\l"? A raw string is also an option.
>   eigenvalue :math:`\lambda` is treated as non-negative if

[Copilot]

Pull request overview

Copilot reviewed 3 out of 3 changed files in this pull request and generated 2 comments.

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