discopt

A Mixed-Integer Nonlinear Programming (MINLP) solver built on a Rust core with Python orchestration. Solves MINLPs by spatial Branch and Bound over rigorous convex relaxations, with an in-house primal/dual simplex for the per-node LPs and a Rust automatic-differentiation tape (via POUNCE) for objective, gradient, Jacobian, and 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; the native Rust spatial B&B kernel is the default engine (DISCOPT_NATIVE_SPATIAL_KERNEL=0 opts back to the Python tree)
• Rust AD tape for NLP evaluation -- objective, gradient, constraint Jacobian, and Lagrangian Hessian (dense and sparse) come from a POUNCE-backed tape with no JAX on the path; DISCOPT_NLP_EVAL=jax restores the legacy JAX evaluator
• In-house LP/MILP engine -- pure-Rust primal/dual simplex with warm starts and a sparse LU basis (feral); HiGHS is no longer on the LP/MILP path
• NLP backends -- POUNCE (pure-Rust Ipopt port, the universal default) and cyipopt (Ipopt); nlp_solver="simplex" selects the pure-Rust warm-started-simplex MILP B&B. The pure-JAX IPM has been retired -- "ipm"/"sparse_ipm" remain as back-compat aliases
• Convex relaxations -- McCormick envelopes over 28 primitive operations (bilinear, powers, exp/log family, trig and inverse-trig, hyperbolics, sigmoid/softplus/tanh, abs/min/max/sign/entropy) plus a 19-intrinsic univariate envelope table in the uniform factorable engine (adding erf, log1p, and the inverse hyperbolics); piecewise McCormick, alphaBB underestimators, and G-convexity / convex-transformable relaxations
• Certified global MINLP -- Adaptive Multivariate Partitioning (solver="amp") for nonconvex bilinear/trilinear/signomial/trig models, and a signomial global optimizer (DISCOPT_SGO) for mixed-sign signomial and integer-signomial problems
• Decomposition solvers -- MIP-NLP family (solver="mip-nlp": OA, ECP, FP, GOA, LP/NLP-BB), Benders and Generalized Benders (GBD), Lagrangian decomposition, and an automatic structure/decomposition advisor
• Derivative-free optimization -- solver="direct" (sampling search over black-box dm.custom bodies) and solver="surrogate" (surrogate-model search); both are explicitly non-certifying, and a governed variant runs as a root heuristic
• Neural network & tree embedding -- embed trained feedforward networks (ReLU, sigmoid, tanh, softplus) as MINLP constraints via big-M, full-space, and reduced-space formulations; decision trees and gradient-boosted ensembles via per-leaf MILP encoding; interval-arithmetic bound propagation; ONNX / scikit-learn / PyTorch readers. Trainable surrogates (nn.trainable, nn.surrogate) emit symbolic weights so a surrogate can be fit simultaneously with a physics model
• 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"), with a disjunct-selection primal constructor on by default
• Complementarity / MPEC -- Model.complementarity(x, y) (elementwise over vectors/arrays) reformulated via GDP disjunction (default), Scholtes regularization, or SOS1
• Bilevel programming -- KKT and strong-duality reformulations of the follower problem, including certified/convex-NLP followers
• Stochastic programming -- extensive form, L-shaped, progressive hedging, multistage, SAA, risk measures, and distributionally-robust variants
• Geometric programming -- posynomial detection with an exact log-space convex reformulation (auto-routed), plus GP-structured MINLPs solved by integer B&B over exact convex log-space node relaxations (solver="gp-minlp")
• 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 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), reverse-FBBT auxiliary cascade, substitution-graph aggregation with postsolve, OBBT with LP warm-start
• Cutting planes -- reformulation-linearization (RLT, a first-class rlt=True option), PSD/SOC cuts for QCQP, GMI cuts, and outer approximation (OA); the structure-gated rlt="auto" policy is the default
• Primal heuristics -- multi-start NLP, feasibility pump, diving, RINS, local branching, QUBO/Ising local search, one-hot swap local search for graph-partition MIQPs
• 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)
• Model import & export -- read AMPL .nl (Rust parser), GAMS .gms, and QPLIB native format; write .nl, .lp, .mps, and GAMS
• Pyomo solver plugin -- use discopt from existing Pyomo models via SolverFactory("discopt") (pip install discopt[pyomo]); see docs/pyomo_solver.md
• GAMS solver link -- run discopt as a GAMS solver through the GMO/GEV API (discopt gams-register, discopt gams-daemon); see docs/gams_solver_link.md
• Warm solve daemon -- discopt solve model.nl routes through a persistent daemon that keeps the process warm across solves
• Dynamic optimization -- DAE collocation (Radau/Legendre), finite differences, and method-of-lines for optimal control, parameter estimation, and PDE-constrained optimization, with multi-experiment trajectory fitting
• Benchmark interfaces -- CUTEst (NLP test set), MINLPLib .nl, and QPLIB (453 quadratic instances, 390 nonconvex, with reference solution vectors)
• LLM integration (optional) -- conversational model building, diagnostics, and reformulation suggestions
• Extensive test suite -- 619 Rust + 7,100+ 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 B&B kernel / TreeManager
                        |                          |
                  NLP evaluation:            Node pool / branching / pruning
                    POUNCE AD tape           In-house primal/dual simplex (node LPs)
                    (default, JAX-free)      Zero-copy numpy arrays (PyO3)
                  NLP backends:
                    pounce  (pure-Rust Ipopt port)  [default]
                    cyipopt (Ipopt)                 [fallback]

Rust backend (crates/discopt-core): Expression IR, Branch and Bound tree (node pool, branching, pruning), the native spatial B&B kernel, in-house primal/dual simplex with a sparse LU basis (feral), .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.

NLP evaluation (python/discopt/_tape_nlp_evaluator.py, _nl_expr_compiler.py): objective, gradient, constraints, Jacobian, and Lagrangian Hessian (dense and sparse) from a POUNCE Rust AD tape. This is the default; expressions with no tape opcode (an opaque dm.custom body, a matrix norm) fall back to the JAX evaluator, and DISCOPT_NLP_EVAL=jax selects it wholesale. A default solve does not import JAX -- not on the LP, QP, MIQP and simplex-MILP paths, and not on the nonlinear ones either.

Relaxation layer (python/discopt/_relax): DAG compiler, the uniform factorable relaxation engine, McCormick convex/concave envelopes, alphaBB, piecewise McCormick, cutting planes, convexity detection, and the relaxation compiler. This layer is numpy: measured over eight nonlinear corpus instances, a default solve loads ~50 _relax modules -- envelope evaluation (uniform_relax, mccormick_lp, incremental_mccormick) and cut separation (cutting_planes, multilinear_separation, psd_cuts) among them -- and zero jax modules. JAX is imported only by the optional differentiable-solve and learned-relaxation subsystems, which are off the default path.

Solver wrappers (python/discopt/solvers): POUNCE (pure-Rust Ipopt port) for LP/QP/NLP, the in-house simplex LP/MILP backends, cyipopt for Ipopt, AMP, the MIP-NLP decomposition family, GDPopt-LOA, the DFO backends (direct, surrogate), and an optional Gurobi backend. highspy is used only on the OA/GDP paths.

Interfaces (python/discopt/interfaces): PyCUTEst-based evaluator for NLP benchmarking against the CUTEst test set, and a native QPLIB reader.

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

NLP Backends

Backend	Implementation	Use Case
pounce (default)	Pure-Rust Ipopt port	Universal default: LP/QP/MILP/MIQP/NLP/MINLP
ipopt / cyipopt	Ipopt via cyipopt	NLP node and continuous solves; most robust
simplex	Pure-Rust warm-started simplex B&B	MILP; the fully JAX-free MILP path
ipm / sparse_ipm	Back-compat aliases	Simplex-first LP/MILP routing; resolve to POUNCE for NLP/MINLP

The pure-JAX interior-point method has been retired. nlp_solver="ipm" is kept as an alias so existing scripts keep working: it selects the simplex-first matrix routing for LP/MILP and resolves to POUNCE for NLP/MINLP.

result = model.solve()                       # default: POUNCE
result = model.solve(nlp_solver="pounce")    # POUNCE (pure-Rust Ipopt port)
result = model.solve(nlp_solver="ipopt")     # Ipopt via cyipopt
result = model.solve(nlp_solver="simplex")   # pure-Rust simplex MILP B&B

Benchmarks

The numbers below are the committed outputs of docs/notebooks/benchmarks_by_class.ipynb, re-executed on the current Rust AD tape backend (Python 3.12, CPU, median of 3 runs including setup). Absolute times are machine-dependent -- the notebook is the reproducible source. All solvers agree on the objective value.

Problem Class	discopt	Comparison	Notes
LP (n=100)	0.234s	HiGHS 0.0015s, scipy 0.0019s	Algebraic extraction, no autodiff
QP (n=100)	0.417s	scipy SLSQP 0.023s	--
MILP (n=25, 8 int)	0.019s	HiGHS MIP 0.0017s	B&B + LP relaxation, correct objectives
MIQP (n=10)	0.018s	forced NLP path 0.707s	QP-specialized path: ~40x speedup
NLP (n=20, Rosenbrock)	POUNCE 0.120s	cyipopt 0.126s	Two implementations of the same IPM
MINLP (n=10)	0.026s (batch=1)	0.026s (batch=16)	These trees close in 1-5 nodes, so batching has nothing to fill

HiGHS (C++ simplex) and scipy remain faster on the LP/MILP classes, as expected for mature production codes; discopt's value on these classes is that they are reachable from the same model object as the MINLP path.

See the benchmark notebooks for full scaling plots and details:

• Benchmarks by Problem Class -- LP, QP, MILP, MIQP, NLP, MINLP
• NLP Backend Comparison -- POUNCE vs Ipopt

Installation

Requires Rust 1.84+ and Python 3.10+. POUNCE -- the default numerical engine -- is a pure-Rust Ipopt port installed as a core dependency, with no system libraries needed. cyipopt is an optional fallback that needs the Ipopt C library.

pip install discopt

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

From a source checkout:

# 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.

Optional extras: ipopt, cutest, gams, llm, sdp, nn (ONNX), pyomo, ml (scikit-learn), xgboost, lightgbm, gnn, learned, sympy, dev, all.

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 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", "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 MILP relaxations on the in-house backends, 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 cyipopt
uv pip install -e ".[dev,ipopt]"
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 JAX/XLA CPU stack used by the relaxation layer 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 the pooling problem in pq-formulation (discopt.pooling). Both moved out of the core package.
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 solve model.nl   # Solve a .nl model (warm-routed through the solve daemon)
discopt convert in.gms out.nl
discopt daemon status    # Control the warm solve daemon (serve/stop/kill/status)
discopt gams-register    # Register discopt as a GAMS solver
discopt gams-daemon      # Control the warm GAMS solver daemon
discopt gams-verify      # Run the packaged .gms corpus through GAMS with solver=discopt
discopt install-skills   # Install Claude Code slash commands and agents

discopt solve accepts the usual solve controls as flags (--profile, --time-limit, --gap, --solver, --rlt, --partitions, --tuning, --json, --sol).

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, Modeling Guide, Sets and Indexing -- basic modeling and solving
• Problem-class tutorials -- LP, QP, MILP, MIQP, MINLP, GDP, DAE, robust, multi-objective, complementarity/MPEC, bilevel, stochastic, pooling, geometric programming
• Solver backends -- OA, MIP-NLP, Benders, GBD, Lagrangian, the decomposition advisor, AMP global MINLP, DIRECT and surrogate DFO, POUNCE, cyipopt, and solver selection
• Advanced Features -- relaxations, presolve, bound tightening, cutting planes, convexity detection, symbolic envelopes, primal heuristics, IIS/conflict analysis, callbacks, warm starts, export formats
• Global Optimization -- which problems discopt can and can't certify as global
• Applications -- neural network embedding, neural DAEs, AC OPF, decision-focused learning, parameter estimation
• Appendix -- solver comparison, the GAMS solver link, references

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

Project Statistics

Last updated: 2026-08-14

Category	Count
Python source (python/discopt/)	333 files, ~170,200 lines
Rust source (crates/)	77 files, ~58,800 lines
Test code (python/tests/)	566 files, ~161,000 lines
Total source + tests	~976 files, ~390,000 lines
Python tests	7,100+
Rust tests	619
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)