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), ripopt (Rust IPM via PyO3), 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)
                    ripopt  (Rust IPM, PyO3)
                    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): ripopt (Rust IPM via PyO3), 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
ripopt	Rust IPM via PyO3	Single-problem NLP; fastest wall-clock
cyipopt	Ipopt via cyipopt	Single-problem NLP; most robust

result = model.solve(nlp_solver="ipm")      # Pure-JAX (default)
result = model.solve(nlp_solver="ripopt")   # Rust 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, ripopt 0.42s, Ipopt 0.43s	--	ripopt 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 ripopt vs Ipopt -- detailed NLP backend comparison
• Batch IPM vs Ipopt -- vmap-batched IPM for B&B inner loops

Installation

Requires Rust 1.84+, Python 3.10+, and Ipopt.

# Install Ipopt (macOS)
brew install ipopt

# Clone ripopt alongside discopt (path dependency at ../ripopt)
git clone <ripopt-repo-url> ../ripopt

# Build Rust-Python bindings (includes ripopt PyO3 bindings)
cd crates/discopt-python && maturin develop && cd ../..

# Run tests
cargo test -p discopt-core
JAX_PLATFORMS=cpu JAX_ENABLE_X64=1 pytest python/tests/ -v

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

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)