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:

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

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

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

All subcommands output structured JSON, making them suitable for scripting and integration with other tools. The discoptbot literature scanner skill uses these subcommands 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)