discopt

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discopt

A hybrid Mixed-Integer Nonlinear Programming (MINLP) solver combining a Rust backend, JAX automatic differentiation, and Python orchestration. Solves MINLP problems via NLP-based spatial Branch and Bound with JIT-compiled objective/gradient/Hessian evaluation.

Features

  • Algebraic modeling API -- continuous, binary, and integer variables with operator overloading
  • Spatial Branch and Bound -- Rust-powered node pool, branching, and pruning
  • JIT-compiled NLP evaluation -- objective, gradient, Hessian, and constraint Jacobian via JAX
  • Three NLP backends -- POUNCE (pure-Rust Ipopt port; default for single solves), pure-JAX interior-point method (vmap-batched B&B node engine), cyipopt (Ipopt)
  • Convex relaxations -- McCormick envelopes (28 functions including sigmoid/softplus/tanh and the trig/inverse-trig/erf families), piecewise McCormick, alphaBB underestimators
  • Neural network embedding -- embed trained feedforward networks (ReLU, sigmoid, tanh, softplus) as MINLP constraints via big-M, full-space, and reduced-space strategies; interval arithmetic bound propagation; ONNX import (pip install discopt[nn])
  • Generalized disjunctive programming -- BooleanVar, propositional logic operators (land, lor, lnot, atleast, atmost, exactly), either_or(), if_then(); reformulated via big-M, multiple big-M (LP-tightened), hull, or Logic-based Outer Approximation (gdp_method="loa")
  • Complementarity / MPEC -- Model.complementarity(x, y) reformulated via GDP disjunction (default), Scholtes regularization, or SOS1
  • Specialized problem classes -- pooling problem (pq-formulation), geometric programming (posynomial detection + log-space convex reformulation), AC optimal power flow (rectangular QCQP)
  • Robust & multi-objective optimization -- uncertainty sets with affine decision rules; scalarization (weighted-sum, ε-constraint, Tchebycheff, NBI, NNC) with Pareto-front analysis
  • Parameter estimation -- weighted-least-squares estimation with exact JAX Fisher-information Jacobians; model-based design of experiments (D/A/E-optimality, identifiability, model discrimination) is available via the discopt-doe plugin
  • Presolve -- FBBT (interval arithmetic, probing, Big-M simplification, integrality-aware snapping, periodic-variable reduction), OBBT with LP warm-start
  • Cutting planes -- reformulation-linearization (RLT, a first-class rlt_cuts=True option), PSD/SOC cuts for QCQP, and outer approximation (OA); cuts='auto' by default
  • Primal heuristics -- multi-start NLP, feasibility pump, diving, RINS, local branching
  • Infeasibility diagnosis -- irreducible infeasible subsystem (compute_iis) and conflict analysis / no-good cuts
  • Differentiable optimization -- parameter sensitivity via envelope theorem and KKT implicit differentiation, including differentiable MILP/MIQP (fix-and-differentiate)
  • .nl file import -- read AMPL-format models via Rust parser
  • Pyomo solver plugin -- use discopt from existing Pyomo models via SolverFactory("discopt") (pip install discopt[pyomo]); see docs/pyomo_solver.md
  • Dynamic optimization -- DAE collocation (Radau/Legendre) and finite differences for optimal control, parameter estimation, and PDE-constrained optimization
  • CUTEst interface -- NLP benchmarking against the CUTEst test set
  • LLM integration (optional) -- conversational model building, diagnostics, and reformulation suggestions
  • Extensive test suite -- 339 Rust + 3,700+ Python test functions

Quick Start

from discopt import Model

m = Model("example")
x = m.continuous("x", lb=0, ub=5)
y = m.continuous("y", lb=0, ub=5)
z = m.binary("z")

m.minimize(x**2 + y**2 + z)
m.subject_to(x + y >= 1)
m.subject_to(x**2 + y <= 3)

result = m.solve()
print(result.status)     # "optimal"
print(result.objective)  # 0.5
print(result.x)          # {"x": 0.5, "y": 0.5, "z": 0.0}

Architecture

Model.solve()  -->  Python orchestrator  -->  Rust TreeManager (B&B engine)
                        |                          |
                  JAX NLPEvaluator           Node pool / branching / pruning
                  NLP backends:              Zero-copy numpy arrays (PyO3)
                    pounce  (pure-Rust Ipopt port)  [default single solve]
                    ipm     (pure-JAX, vmap batch)  [B&B node relaxations]
                    cyipopt (Ipopt)

Rust backend (crates/discopt-core): Expression IR, Branch and Bound tree (node pool, branching, pruning), .nl file parser, FBBT/presolve (interval arithmetic, probing, Big-M simplification).

Rust-Python bindings (crates/discopt-python): PyO3 bindings with zero-copy numpy array transfer for the B&B tree manager, expression IR, batch dispatch, and .nl parser.

JAX layer (python/discopt/_jax): DAG compiler mapping modeling expressions to JAX primitives, JIT-compiled NLP evaluator (objective, gradient, Hessian, constraint Jacobian), McCormick convex/concave relaxations (28 functions), and a relaxation compiler with vmap support.

Solver wrappers (python/discopt/solvers): POUNCE (pure-Rust Ipopt port), cyipopt NLP wrapper for Ipopt, HiGHS LP and MILP wrappers with warm-start support.

CUTEst interface (python/discopt/interfaces/cutest.py): PyCUTEst-based evaluator for NLP benchmarking against the CUTEst test set.

Orchestrator (python/discopt/solver.py): End-to-end Model.solve() connecting all components. At each B&B node: solve continuous NLP relaxation with tightened bounds, prune infeasible nodes, fathom integer-feasible solutions, branch on most fractional variable.

NLP Backends

Backend Implementation Use Case
pounce (default) Pure-Rust Ipopt port Single-problem NLP; fastest wall-clock
ipm Pure-JAX IPM B&B inner loop; GPU-batched via jax.vmap
cyipopt Ipopt via cyipopt Single-problem NLP; most robust

For single continuous solves the default NLP backend resolves to a KKT-valid solver -- POUNCE when installed, falling back to cyipopt, then to the pure-JAX IPM. The pure-JAX ipm remains the vmap-batched engine for B&B node relaxations.

result = model.solve()                       # default: POUNCE when installed
result = model.solve(nlp_solver="pounce")    # POUNCE (pure-Rust Ipopt port)
result = model.solve(nlp_solver="ipm")       # Pure-JAX IPM
result = model.solve(nlp_solver="cyipopt")   # Ipopt

Benchmarks

Performance measured on Apple M4 Pro (CPU, JAX 0.8.2). "Warm" times exclude JIT compilation. All solvers produce matching objective values.

Problem Class discopt Comparison Notes
LP (n=100) 0.015s warm HiGHS 0.002s, scipy 0.002s Algebraic extraction, no autodiff
QP (n=100) 0.04s warm scipy SLSQP 0.02s Was 66s before algebraic extraction
MILP (n=25) 0.002s HiGHS MIP 0.002s B&B + LP relaxation, correct objectives
MIQP (n=10) 0.004s NLP path 4.9s QP-specialized path: 1000x+ speedup
NLP (n=20, Rosenbrock) IPM 1.1s warm, POUNCE 0.42s, Ipopt 0.43s -- POUNCE fastest single-solve; IPM best for batched B&B
MINLP (n=10) 0.9s (batch=1) 0.9s (batch=16) vmap batching helps with deeper B&B trees

See the benchmark notebooks for full scaling plots and details:

Installation

Requires Rust 1.84+ and Python 3.10+. POUNCE (the default single-solve NLP backend) is a pure-Rust Ipopt port with no system dependencies; cyipopt is an optional fallback that needs the Ipopt C library.

# Install the POUNCE NLP backend (pure-Rust Ipopt port)
pip install pounce-solver

# Optional cyipopt fallback (needs the Ipopt C library; macOS: brew install ipopt)
pip install "discopt[ipopt]"

# Build Rust-Python bindings
cd crates/discopt-python && maturin develop && cd ../..

# Run the fast default PR battery
cargo test -p discopt-core
JAX_PLATFORMS=cpu JAX_ENABLE_X64=1 make test

make test matches the PR CI gate: ordinary non-slow tests plus the pr_correctness subset. Full correctness, integration, and benchmark markers remain available through the explicit Make targets.

Solving nonconvex MINLPs with AMP

For problems with nonconvex nonlinearities (bilinear, trilinear, signomial, trig), the default branch-and-bound path only certifies optimality when the relaxation is convex. The Adaptive Multivariate Partitioning (AMP) solver gives discopt a certified-global path for these problems:

import discopt.modeling as dm

m = dm.Model("concave_qp")
c = [-1.0, 0.5, 1.5]
xs = [m.continuous(f"x{i}", lb=-2.0, ub=2.0) for i in range(3)]
m.subject_to(sum(xs) >= -1.0)
m.subject_to(sum(xs) <= 3.0)
m.minimize(sum(-((xs[i] - c[i]) ** 2) for i in range(3)))  # concave

result = m.solve(solver="amp", rel_gap=1e-4)
print(result.status, result.objective, result.gap)

AMP iterates a piecewise-McCormick / convex-hull MILP relaxation against an NLP subproblem (Ipopt) and refines the partition where the relaxation gap is largest. At every iteration LB_k <= global_opt <= UB_k, so termination at gap <= rel_gap yields a certified global optimum.

Common tuning knobs (all keyword-only on Model.solve(solver="amp", ...)):

Option Default Effect
rel_gap 1e-4 Relative optimality gap stop criterion
max_iter 100 Hard cap on partition-refinement iterations
n_init_partitions 4 Initial partitions per discretized variable
convhull_formulation "disaggregated" "sos2" or "facet" for tighter relaxations
convhull_ebd False Logarithmic Gray-code embedded SOS2 binaries
presolve_bt True OBBT/FBBT bound tightening before the first MILP
obbt_at_root True Strengthen variable bounds at the root
milp_solver "auto" MILP master backend: "auto", "highs", "pounce", "simplex", or "gurobi"
partition_method "adaptive" How to pick which variable/interval to refine

Gurobi can be used as AMP's MILP-master subsolver without changing the global algorithm:

result = m.solve(solver="amp", milp_solver="gurobi", rel_gap=1e-4)

This does not translate general nonlinear expressions into Gurobi nonlinear constraints; discopt still builds and certifies the global MINLP relaxation.

A worked end-to-end example with a non-trivially nonconvex model and the tuning knobs above is in docs/notebooks/amp_global_minlp.ipynb.

AMP Test Suites

Routine AMP development uses a fast default regression battery. The fast environment uses solver-independent checks plus HiGHS-backed MILP relaxations, and excludes optional cyipopt, longer Alpine, MINLPTests, and incidence-style AMP benchmark coverage. AMP and PR-fast Make targets run pytest through scripts/run_memory_capped_pytest.sh, which applies a 32 GB address-space cap with prlimit when available. Override with PYTEST_MEMORY_LIMIT_MB=..., or set PYTEST_MEMORY_LIMIT_MB=0 to disable the cap. The broad make test-quick dev-loop target remains uncapped and excludes memory_heavy tests.

make test-amp-fast

Alpine-reference, MINLPTests, cyipopt, and incidence-style AMP checks are opt-in because they can require optional solvers and longer solve budgets:

# Uses a fresh .venv and pixi-provided solver libraries rather than a local Python env.
pixi exec -s python=3.12 -s ipopt -s pkg-config -s c-compiler -s cxx-compiler -s gfortran -- \
  uv venv --allow-existing .venv
source .venv/bin/activate
uv pip install maturin pytest pytest-timeout numpy scipy jax jaxlib highspy cyipopt
uv pip install -e ".[dev,ipopt,highs]"
maturin develop
make test-amp-integration

For WSL or memory-constrained machines, keep PR-fast AMP/JAX runs capped and use a bounded xdist worker count rather than -n auto. For the single-process AMP integration suite, disable the virtual-address cap to avoid XLA std::bad_alloc aborts from address-space reservations:

PYTEST_MEMORY_LIMIT_MB=32768 PYTEST_XDIST_WORKERS=2 make test
PYTEST_MEMORY_LIMIT_MB=0 make test-amp-integration

WSL users should also set explicit memory and swap limits in .wslconfig so a single uncapped compile-heavy test cannot restart the host session. A stricter 12 GB cap is useful for reproducing memory pressure, but the current JAX/XLA CPU stack can reserve more than 12 GB of virtual address space during AMP runs; use the memory_heavy marker selection when running with tighter caps.

The full Python test suite remains available with make test-all.

Plugins

discopt keeps its core lean and ships domain-specific application builders and teaching tools as separate plugin packages. Each is a PEP 420 namespace package: once installed, its modules import under discopt.<name> unchanged, and any CLI verbs it registers (through the "discopt.cli" entry-point group) become available as discopt <subcommand>. Some are on PyPI; the rest install directly from the repository.

Plugin Install Provides
discopt-doe pip install discopt-doe Model-based design of experiments — D/A/E-optimality, identifiability, model discrimination — as a discopt doe ... CLI loop (templates/new/status/fit/extend/gui) around an .xlsx workbook, with an optional Streamlit GUI.
discopt-aggregation pip install discopt-aggregation Variable aggregation (reduced-space presolve): substitutes variables defined by equality constraints to yield a smaller reduced-space formulation, then recovers them from the solution (Naik et al., arXiv:2502.13869). Exposes aggregate/solve under discopt.aggregation.
discopt-apps pip install "git+https://github.com/jkitchin/discopt-apps.git" Application builders for the modeling language: AC optimal power flow (discopt.opf) and pooling (discopt.pooling).
discopt-course pip install "git+https://github.com/jkitchin/discopt-course.git" An optimization course plus an interactive discopt tutor ... CLI (discopt.course) that walks through modeling and solving exercises. 
# Example: add the design-of-experiments plugin
pip install discopt-doe
discopt doe --help          # the plugin's verbs are now under the `discopt` CLI

Dependent packages are tracked in .github/dependents.yml; each discopt release automatically re-runs their CI and opens a review issue so breakage surfaces early (see docs/dev/dependents.md).

Writing a plugin? You can have discopt automatically exercise your package against every new core release. Ask to be added to .github/dependents.yml, and copy .github/dependent-ci-template.yml into your repo as .github/workflows/discopt-integration.yml — it listens for the discopt-updated dispatch and runs your tests against discopt main (with a weekly fallback), so you find out immediately if a discopt release breaks you. Details in docs/dev/dependents.md.

Command-Line Interface

After installation, the discopt command is available on your PATH:

discopt about            # Version and installation info
discopt test             # Smoke-test the install
discopt convert in.gms out.nl
discopt install-skills   # Install Claude Code slash commands and agents

External packages can add subcommands through the "discopt.cli" entry-point group (see the protocol notes in python/discopt/cli.py). For example, the discopt-doe plugin (pip install discopt-doe) adds discopt doe ... — a model-based design-of-experiments loop (templates/new/status/fit/extend/gui) around an .xlsx workbook, with an optional Streamlit GUI. See Plugins above for the full list.

A separate discopt-dev script ships developer-only commands used from inside a discopt source checkout (literature scanner, adversary tester, the arXiv / OpenAlex search helpers and the report writer they call):

# Search arXiv for recent papers
discopt-dev search-arxiv 'all:"spatial branch and bound"' --max-results 10 --start-date 2026-01-01

# Search OpenAlex
discopt-dev search-openalex "McCormick relaxation" --from-date 2026-01-01 --to-date 2026-03-31

# Write a report from stdin
echo "report content" | discopt-dev write-report reports/output.md

All discopt-dev search subcommands output structured JSON. The /discoptbot literature-scanner slash command uses them to automatically find and summarize relevant new papers from arXiv and OpenAlex.

Documentation

Tutorial notebooks are available in docs/notebooks/:

  • Quickstart -- basic modeling and solving
  • MINLP Examples -- mixed-integer nonlinear programs
  • Advanced Features -- relaxations, presolve, cutting planes, branching policies
  • Global Optimization -- which problems discopt can and can't certify as global
  • IPM vs Ipopt -- backend comparison (incl. vmap-batched IPM)
  • Dynamic Optimization -- DAE collocation for optimal control, parameter estimation, and PDEs
  • Neural Network Embedding -- optimize over trained ML surrogates as MINLP constraints
  • Decision-Focused Learning -- differentiable optimization in ML pipelines
  • GDP Tutorial -- disjunctive programming, logical constraints, big-M/hull/LOA reformulations

Full documentation is built with Jupyter Book: jupyter-book build docs/

Project Statistics

Last updated: 2026-06-18

Category Count
Python source (python/discopt/) 226 files, ~103,700 lines
Rust source (crates/) 55 files, ~29,000 lines
Test code (python/tests/) 222 files, ~72,100 lines
Total source + tests ~500 files, ~205,000 lines
Python tests 3,700+
Rust tests 339
Tutorial notebooks (docs/notebooks/) 63

Development History

See ROADMAP.md for the full development roadmap and task history.

License

Eclipse Public License 2.0 (EPL-2.0)

Project links

Data verified by PyPI on Jul 24, 2026
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  • Released:
Newer release available (0.8.0)

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Avatar for jkitchin from gravatar.com jkitchin

Credits

Author: John Kitchin

GitHub Statistics

Data verified by PyPI on Jul 24, 2026
The GitHub source repository was provided by the project maintainers and verified by PyPI at the time of upload. Stars, forks, and open issues/PRs are derived from that repository and have not been independently verified.

License

Eclipse Public License 2.0 (EPL-2.0) (EPL-2.0)

Requires

Python >=3.10

Provides Extra

all cutest dev gams gnn ipopt learned lightgbm llm ml nn pounce pyomo sdp sympy xgboost

Tags

optimization MINLP branch-and-bound nonlinear solver JAX

Classifiers

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0.8.0

12 files

This release

0.7.0 This release

12 files

0.6.0

12 files

0.5.0

12 files

0.4.0

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0.3.0

12 files

0.2.5

12 files

0.2.4

12 files

0.2.3

12 files

0.2.2

11 files

0.2.1

11 files

0.2.0

11 files

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