Variable aggregation (reduced-space presolve) for nonlinear optimization — a standalone plugin for discopt that installs into the discopt.aggregation namespace.

📖 Documentation

It implements Naik, Biegler, Bent & Parker, Variable aggregation for nonlinear optimization problems (arXiv:2502.13869): substitute variables defined by equality constraints into the rest of a model, eliminating both a variable and a constraint to yield a smaller reduced-space formulation, then recover the eliminated variables from the reduced solution.

import discopt.modeling as dm
from discopt.aggregation import aggregate, solve

m = dm.Model("example")
x = m.continuous("x", lb=-5, ub=5)
y = m.continuous("y", lb=-5, ub=5)
m.subject_to(y - (x + 1) == 0.0)          # y is defined by x
m.minimize(x**2 + y**2)

res = solve(m, method="d2")                # aggregate → solve → recover
print(res.status, res.objective)          # optimal 0.5
print(res.x)                              # {'x': -0.5, 'y': 0.5}  (y recovered)

Installation

pip install discopt-aggregation          # from PyPI

Or from a checkout for development:

uv pip install -e ".[dev]"               # or: pip install -e ".[dev]"

Requires discopt >= 0.6. The plugin is a discopt.aggregation namespace package: it merges into the installed discopt package at import time. This needs discopt/__init__.py to extend its search path, i.e. to contain:

__path__ = __import__("pkgutil").extend_path(__path__, __name__)

discopt 0.6+ includes this line. (If you use an older discopt, add it once.)

Claude skill

This package ships a Claude Code skill that documents how to use aggregation (method choice, the structure-preserving vs Hessian-cost tradeoff, every option, recovery, diagnostics, the study harnesses). Claude Code does not auto-discover skills from installed Python packages, so after pip install run the bundled installer once to copy it into a .claude/skills/ directory Claude scans:

discopt-aggregation-skill install            # -> ./.claude/skills/  (this project)
discopt-aggregation-skill install --user     # -> ~/.claude/skills/  (every project)
discopt-aggregation-skill path               # where the packaged skill lives

Working inside this repo, the skill is already at .claude/skills/ (no install needed). The repo is also a Claude Code plugin (.claude-plugin/plugin.json

• skills/), so it can be loaded with claude --plugin-dir <repo> or published to a marketplace. The single source of truth is src/discopt/aggregation/skill/; the two .claude/skills / skills entries are symlinks to it.

Methods

method= selects the strategy, most conservative to most aggressive:

key	name	eliminates	paper
ld1	fixed-variable (degree-1)	y = a	Alg 3
ecd2	equal-coefficient degree-2	y = x + a	Alg 6
ld2	linear degree-2	y = a*x + b	Alg 5
d2	degree-2 (default)	y = f(x) (≤ 2 variables)	Alg 4
gr	greedy	y = f(w, x, …) (y linear)	Alg 1
lm	linear-matching	y = f(w, x, …) (y linear)	Alg 2

ld1/ecd2/ld2/d2 are structure-preserving; gr/lm are approximate-maximum. The paper recommends d2; it is the default.

Integer aggregation (opt-in, beyond the paper)

By default only scalar continuous variables are eliminated. Pass aggregate(..., integer_aggregation=True) (or solve(...)) to also eliminate a scalar integer/binary variable — but only when its integrality is implied, the standard MIP-presolve condition (Achterberg et al. 2020): the defining equality is fully affine, the pivot coefficient is ±1, every other variable in it is integer/binary, and every other coefficient and the constant are integral (e.g. an all-integer stock balance s[t] = s[t-1] + q[t] - d[t]). Recovery returns exactly integral values; dual recovery reports available=False over eliminated integers. The flag is default-off and never eliminates a variable it cannot prove integral (fractional data, non-unit pivot, or a continuous participant all abstain), so the default behaviour is unchanged.

Features

• Six strategies, each producing a strictly lower-triangular aggregation set (Lemma 1) with explicit, solve-free post-solve recovery.
• Numerical safeguards: a relative pivot tolerance (pivot_tol) against ill-conditioned substitutions, and an optional fill-in cap (max_fill).
• Redundant-bound pruning (prune_bounds, on by default): box→inequality constraints proven redundant by interval propagation are omitted.
• Array support (scalarize, on by default): fully-indexed array variables are scalarized so aggregation reaches discretized (DAE) models, then arrays are reassembled on recovery.
• Structural metrics (compare_methods) reproducing the paper's Table 4, including the exact AD Hessian nonzero count.

Examples

python -m discopt.aggregation.examples runs commented, executable walkthroughs of every method, the recursive pipeline, end-to-end solve + recovery, the structural comparison, the safeguards, array scalarization, and a performance/scaling demo.

Tests

uv pip install -e ".[dev]"
python -m pytest tests/ -q          # the full suite

Layout

src/discopt/aggregation/    # the plugin (PEP 420 namespace subpackage)
  core:        matching · incidence · strategies · transform · recovery · api
  walking:     exprwalk (single DAG-walk authority for all analyses)
  structure:   scalarize · metrics · diagnostics (Dulmage–Mendelsohn) · ordering
  numerics:    guards · hessian_cost · duals · derivatives · implicit · tearing · schur
  study:       testproblems · benchmark · sweep · profiling · presolve · examples
tests/                      # test_aggregation_*.py
design/                     # follow-up roadmap · parity plan · references.bib

References

Primary:

Sakshi Naik, Lorenz Biegler, Russell Bent, Robert Parker. Variable aggregation for nonlinear optimization problems. arXiv:2502.13869 (2025). https://arxiv.org/abs/2502.13869

The full set of related work — reduced-space / implicit elimination (Parker et al. 2022), block-triangular KKT (Parker, Garcia & Bent 2026), exact tearing / minimum feedback set (Baharev et al. 2021), Dulmage–Mendelsohn debugging (Parker et al. 2023), and the MIP-presolve line (Achterberg et al. 2020) — is collected as verified BibTeX in design/references.bib, and cited from the design docs under design/.

Contributing

See CONTRIBUTING.md for dev setup, the lint/type/test gate, and the project conventions (keep discopt/pounce/feral untouched, new behavior opt-in/default-off, a worked example per feature, hash-seed-robust tests).

License

MIT License. See LICENSE.