cuopt-numerical-optimization-api

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Audit 0.4.1 · source sha 0d80e4f109d7 · 29 Oct 2026Report an issue or request a re-scan

• Publishernvidia GitHub organizationOwner of the repository this skill is read from
• Source foldernvidia/skills/skills/cuopt-numerical-optimization-apiThe exact folder we audited
• LicenceApache-2.0As the repository states it
• Commit pinned for this verdict0d80e4f109d7A new audit runs when the source changes
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Its description: LP, MILP, and QP (beta) with cuOpt — Python, C, and CLI. Use when the user is solving LP, MILP, or QP with any cuOpt interface.

---
name: cuopt-numerical-optimization-api
version: "26.10.00"
description: LP, MILP, and QP (beta) with cuOpt — Python, C, and CLI. Use when the user is solving LP, MILP, or QP with any cuOpt interface.
license: Apache-2.0
metadata:
  author: NVIDIA cuOpt Team
  tags:
    - cuopt
    - linear-programming
    - milp
    - qp
    - python
    - c-api
    - cli
---



# cuOpt Numerical Optimization API

Model and solve LP, MILP, and QP problems using NVIDIA cuOpt's GPU-accelerated solver.

## Interface Selection

Choose the reference for the user's interface:

| Interface | When to use | Reference |
|-----------|-------------|-----------|
| **Python** | User is writing Python code | [references/python_api.md](references/python_api.md) |
| **C / C++** | User is embedding in a C/C++ application | [references/c_api.md](references/c_api.md) |
| **CLI** | User is solving from MPS files on the command line | [references/cli_api.md](references/cli_api.md) |

If the interface is not yet clear, ask before writing any code.

**Already using a modeling language?** cuOpt also works as a solver backend for third-party
modeling tools — **AMPL, GAMS / GAMSPy, PuLP, JuMP, Pyomo, and CVXPY** — with near-zero code
changes (point the model's solver at cuOpt). CVXPY additionally covers convex QP and, in beta,
QCQP / SOCP. Prefer this when the user already has a model in one of these tools rather than porting
it to the cuOpt API. See
[Third-Party Modeling Languages](https://docs.nvidia.com/cuopt/user-guide/latest/thirdparty_modeling_languages/index.html).

## Choosing LP vs MILP vs QP

**Decide from the objective and variables:**

| If the objective is... | And variables are... | Use |
|---|---|---|
| Linear (sum of `c_i * x_i`) | All continuous | **LP** |
| Linear | Some integer or binary | **MILP** |
| Has squared (`x*x`) or cross (`x*y`) terms | Continuous (integer QP not supported) | **QP** (beta) |

**Prefer LP when the problem allows it.** LP solves faster and has stronger optimality guarantees. Use MILP only when the problem logically requires whole numbers or yes/no decisions. Use QP only when the objective is genuinely quadratic (variance, squared error, kinetic energy).

- **Use LP** when every quantity can meaningfully be fractional: flows, proportions, rates, dollars, hours, tonnes of material, etc.
- **Use MILP** when the problem mentions **counts** of discrete entities, **yes/no** choices, or **either/or** decisions (e.g. open a facility or not, assign a person to a shift, number of trucks).
- **Use QP** when the objective minimizes variance, squared error, or any expression with `x*x` or `x*y` terms (portfolio optimization, least squares, regularized regression).

## Integer vs Continuous from Wording

| Problem wording / concept | Variable type | Examples |
|---------------------------|---------------|----------|
| **Discrete entities (counts)** | **INTEGER** | Workers, cars, trucks, machines, pilots, facilities, units to manufacture |
| **Yes/no or on/off** | **INTEGER** (binary, lb=0 ub=1) | Open a facility, run a machine, assign a person to a shift |
| **Amounts that can be fractional** | **CONTINUOUS** | Tonnes, litres, dollars, hours, kWh, proportion of capacity |
| **Rates or fractions** | **CONTINUOUS** | Utilization, percentage, share of budget |

**Rule of thumb:** "How many *things*" → INTEGER. "How much" → CONTINUOUS.

## QP Rules (all interfaces)

- **MINIMIZE only** — the solver rejects MAXIMIZE for quadratic objectives. To maximize `f(x)`, minimize `-f(x)` and negate the reported objective value.
- **Continuous variables only** — integer QP is not supported.
- **Q should be positive semi-definite** for a convex, well-posed problem.
- **Beta** — API may evolve; treat as production-capable for typical convex QP.

## Dual Values

Duals and reduced costs are available for **LP and QP only**:
- **MILP** — no duals (integer optima are not continuous).
- **Quadratic constraints** — duals unavailable even for LP/QP; all values return `NaN`.
- **PDLP warmstart** — LP only; MILP solves do not accept a PDLP warmstart.

## Common Issues (all interfaces)

| Problem | Likely cause | Fix |
|---------|-------------|-----|
| Infeasible | Conflicting constraints | Check constraint logic and bounds |
| Unbounded | Missing bounds | Add variable bounds |
| Slow solve | Large problem | Set time limit; increase gap tolerance |
| QP rejected with MAXIMIZE | QP only supports MINIMIZE | Negate the objective; negate the result |
| QP returns non-optimal | Q not PSD or badly scaled | Check Q is PSD; rescale variables |

## Solver Settings (concepts)

| Setting | Purpose |
|---------|---------|
| `time_limit` | Stop after N seconds |
| `mip_relative_gap` | Stop MILP when within X% of optimal |
| `mip_absolute_tolerance` | Absolute MIP gap stop |
| `log_to_console` | Enable solver logging |

Syntax varies by interface — see the interface reference file.

Excerpt, first 4,922 characters of SKILL.md, verbatim from the audited commit. It is text from someone else’s repository, quoted so you can judge it before your agent reads it.

1. 2026-10-29
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   first audit · source 0d80e4f109d7

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