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:

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.

Choosing LP vs MILP vs QP

Decide from the objective and variables:

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

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)

Solver Settings (concepts)

Syntax varies by interface — see the interface reference file.