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 -- pure-JAX interior-point method (default, vmap-batched), POUNCE (pure-Rust Ipopt port), cyipopt (Ipopt)
• Convex relaxations -- McCormick envelopes (21 functions including sigmoid/softplus/tanh), 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")
• Presolve -- FBBT (interval arithmetic, probing, Big-M simplification), OBBT with LP warm-start
• Cutting planes -- reformulation-linearization (RLT) and outer approximation (OA)
• GNN branching policy -- bipartite graph neural network trained on strong branching data
• Primal heuristics -- multi-start NLP, feasibility pump
• Differentiable optimization -- parameter sensitivity via envelope theorem and KKT implicit differentiation
• .nl file import -- read AMPL-format models via Rust parser
• 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
• 1650+ tests -- 141 Rust + 1510+ Python

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)
                    ipm     (pure-JAX, vmap batch)  [default]
                    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 (21 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
ipm (default)	Pure-JAX IPM	B&B inner loop; GPU-batched via jax.vmap
pounce	Pure-Rust Ipopt port	Single-problem NLP; fastest wall-clock
cyipopt	Ipopt via cyipopt	Single-problem NLP; most robust

For single continuous solves the ipm default is promoted to a KKT-valid backend, resolving to POUNCE when installed and falling back to cyipopt.

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

• Benchmarks by Problem Class -- LP, QP, MILP, MIQP, NLP (3 backends), MINLP
• IPM vs POUNCE vs Ipopt -- detailed NLP backend comparison
• Batch IPM vs Ipopt -- vmap-batched IPM for B&B inner loops

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
partition_method	"adaptive"	How to pick which variable/interval to refine

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 16 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 broad AMP/JAX runs capped and use a bounded xdist worker count rather than -n auto:

PYTEST_MEMORY_LIMIT_MB=16384 PYTEST_XDIST_WORKERS=2 make test
PYTEST_MEMORY_LIMIT_MB=16384 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.

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
discopt doe ...          # Model-based design of experiments (5-verb loop)

DoE from the command line

discopt doe drives a model-based design-of-experiments loop around a single .xlsx workbook that travels between the lab bench and the CLI. Five verbs cover the full cycle:

# 1. List the built-in templates (linear, polynomial-1d,
#    response-surface-2d, response-surface-3d).
discopt doe templates

# 2. Generate an initial optimal design.
discopt doe new response-surface-2d \
    --input temp:50:100 --input ph:3:9 \
    --response yield --error 0.5 --n 6 -o campaign.xlsx

# 3. (Run the experiments; fill the `yield` column in campaign.xlsx; save.)
discopt doe status campaign.xlsx

# 4. Fit parameters from the completed runs (writes parameters + FIM sheets).
discopt doe fit campaign.xlsx

# 5. Append a next batch of D-optimal runs that reuse the fitted FIM.
discopt doe extend campaign.xlsx --n 4

Every verb also takes --json for LLM agent or GUI consumption. The workbook is the single source of truth — status, fit, and extend only need the file path. An --module pkg.mod:MyExperiment escape hatch on new swaps the template for any custom Experiment subclass. Install the optional dependency with pip install discopt[doe].

A Streamlit GUI over the same workflow ships under pip install 'discopt[doe-gui]':

discopt doe gui                # blank slate; create or open from sidebar
discopt doe gui campaign.xlsx  # drop straight into an existing campaign

The GUI binds directly to the same do_* functions the CLI uses, so both surfaces stay in lockstep automatically.

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
• IPM vs Ipopt -- backend comparison
• Batch IPM -- vmap-batched interior-point solving
• 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: 2026-02-16

Category	Count
Python source (python/discopt/)	65 files, ~27,200 lines
Rust source (crates/)	19 files, ~10,700 lines
Test code (python/tests/)	41 files, ~24,500 lines
Total source + tests	125 files, ~62,400 lines
Python tests	1,510+
Rust tests	141
Tutorial notebooks (docs/notebooks/)	21
Git commits	99

Development History

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

License

Eclipse Public License 2.0 (EPL-2.0)