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Variable aggregation is a reduced-space presolve for nonlinear optimization: it substitutes 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 recovers the eliminated variables (and their duals) from the reduced solution.

discopt-aggregation is a standalone plugin for discopt that installs into the discopt.aggregation namespace. It implements Naik, Biegler, Bent & Parker, Variable aggregation for nonlinear optimization problems (arXiv:2502.13869).

Quickstart

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)

  • Get started

    Install the plugin and run your first reduced-space solve.

    Installation

  • Choose a method

    Six strategies from conservative fixed-variable elimination to approximate-maximum matching.

    Methods

  • Tune & recover

    Numerical guards, bound pruning, array support, primal & dual recovery.

    Options & recovery

  • Study & reproduce

    Structural metrics, benchmarks, and reliability sweeps reproducing the paper's tables.

    Study & benchmarks

Why aggregate?

A model often carries intermediate variables that are defined by an equality constraint — a discretized DAE state, a recycle stream, an algebraic rate. Each such definition is a variable and a constraint the solver must carry. Substituting the definition removes both, shrinking the problem the interior-point solver sees and often improving its conditioning and convergence — at zero cost to the optimum, because every strategy produces a strictly lower-triangular aggregation set (Lemma 1) with explicit, solve-free post-solve recovery.

Features

  • Six strategies, most conservative to most aggressive: ld1, ecd2, ld2, d2 (default), gr, lm. See Methods.
  • Numerical safeguards: a relative pivot tolerance against ill-conditioned substitutions, an optional fill-in cap, and derivative-amplification / condition guards.
  • Redundant-bound pruning by interval propagation (on by default).
  • Array support: fully-indexed array variables are scalarized so aggregation reaches discretized (DAE) models, then reassembled on recovery.
  • Primal & dual recovery, including recursive multi-pass duals.
  • Integer aggregation (opt-in, beyond the paper): eliminate a scalar integer/binary variable when its integrality is implied. See Integer aggregation.
  • Structural metrics & study harnesses reproducing the paper's Table 4 and the reliability figures.

Citation

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