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Correct dual-value scope to LP/QP in numerical-optimization API skills #1408

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Correct dual-value scope to LP/QP in numerical-optimization API skills
cafzal Jun 8, 2026
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Address review: remove duplicate Duals note from api-c assets/README
cafzal Jun 9, 2026
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Address review: minimize per reviewer feedback
cafzal Jun 9, 2026
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8 changes: 8 additions & 0 deletions skills/cuopt-numerical-optimization-api-c/SKILL.md
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Expand Up @@ -35,6 +35,14 @@ QP uses the same library, include/lib paths, and build pattern as LP/MILP — on
- **Continuous variables only** — set `CUOPT_CONTINUOUS` for every variable; integer QP is not supported.
- **Q should be PSD** for a convex problem.

## Dual values (LP / QP)

`cuOptGetDualSolution` (shadow prices) and `cuOptGetReducedCosts` (reduced costs) return values

@mlubin mlubin Jun 9, 2026

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I'm going to continue my push against "shadow prices". I don't think the parentheticals are necessary here. cuOptGetDualSolution returns duals and cuOptGetReducedCosts returns reduces costs. Readers can look at the function documentation for more information.

@cafzal cafzal Jun 9, 2026

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Good point. Removed. I commit to no more 'shadow prices' too 😆

for **LP and QP with linear constraints** — the barrier solver is primal-dual, so a quadratic

@mlubin mlubin Jun 9, 2026

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No need to say anything about the barrier solver. The solve method isn't part of the API contract for duals.

@cafzal cafzal Jun 9, 2026

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Resolved.

objective still yields duals. cuOpt returns **no duals for a problem with quadratic constraints**
(the returned arrays are filled with `NaN`). See [assets/lp_duals](assets/lp_duals/) for the call
sequence — it is an LP, but the same calls apply to a QP whose constraints are all linear.

@coderabbitai coderabbitai Bot Jun 9, 2026

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⚠️ Potential issue | 🟠 Major

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In `@skills/cuopt-numerical-optimization-api-c/SKILL.md` around lines 38 - 44,
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Source: Coding guidelines


## Debugging (MPS / C)

**MPS parsing:** Required sections in order: NAME, ROWS, COLUMNS, RHS, (optional) BOUNDS, ENDATA. Integer markers: `'MARKER'`, `'INTORG'`, `'INTEND'`.
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5 changes: 5 additions & 0 deletions skills/cuopt-numerical-optimization-api-c/assets/README.md
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Expand Up @@ -11,6 +11,11 @@ LP/MILP C API reference implementations. Use as reference when building new appl
| [milp_production_planning](milp_production_planning/) | MILP | Production planning with resource constraints |
| [mps_solver](mps_solver/) | LP/MILP | Solve from MPS file via `cuOptReadProblem` |

> **Duals:** `lp_duals` is an LP, but `cuOptGetDualSolution` / `cuOptGetReducedCosts` also return

@ramakrishnap-nv ramakrishnap-nv Jun 9, 2026

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Suggested change
> **Duals:** `lp_duals` is an LP, but `cuOptGetDualSolution` / `cuOptGetReducedCosts` also return
**Duals:** `lp_duals` is an LP, but `cuOptGetDualSolution` / `cuOptGetReducedCosts` also return

same for other lines as well

@ramakrishnap-nv ramakrishnap-nv Jun 9, 2026

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If we have similar workding in skills, do we need to update in README again?

@cafzal cafzal Jun 9, 2026

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Removed the note entirely instead of reformatting — it duplicated the Dual values (LP / QP) section now in SKILL.md. Thanks for catching it.

@cafzal cafzal Jun 9, 2026

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Good call — no need to state it in both. Removed it from the README; the SKILL.md section is the single source.

> shadow prices and reduced costs for a **QP with linear constraints** (the barrier solver is
> primal-dual). No duals are returned for problems with **quadratic constraints** — the arrays
> come back filled with `NaN`.

## Build and run

Set include and library paths, then build and run.
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12 changes: 9 additions & 3 deletions skills/cuopt-numerical-optimization-api-python/SKILL.md
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Expand Up @@ -253,12 +253,18 @@ settings.set_parameter("log_to_console", 1)
| QP rejected with MAXIMIZE | QP only supports MINIMIZE | Negate the objective: minimize `-f(x)` |
| QP returns non-optimal | Q not PSD or variables badly scaled | Check Q is PSD; rescale variables to similar magnitudes |

## Getting Dual Values (LP only)
## Getting Dual Values (LP / QP)

Shadow prices (`DualValue`) and reduced costs (`ReducedCost`) are returned for **LP and QP** —

@mlubin mlubin Jun 9, 2026

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Duals and reduced costs (no parentheticals)

@cafzal cafzal Jun 9, 2026

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Resolved.

cuOpt's barrier solver is primal-dual, so a QP with a quadratic objective and **linear**
constraints returns duals just like an LP. The constraints you read duals from must be linear:
cuOpt returns **no dual variables for a problem that has any quadratic constraint** (every
`DualValue`/`ReducedCost` comes back as `NaN`). MILP returns no duals.

```python
if problem.Status.name == "Optimal":
constraint = problem.getConstraint("resource_a")
shadow_price = constraint.DualValue
constraint = problem.getConstraint("resource_a") # linear constraint
shadow_price = constraint.DualValue # NaN if the model has quadratic constraints
print(f"Shadow price: {shadow_price}")
```

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30 changes: 30 additions & 0 deletions skills/cuopt-numerical-optimization-api-python/references/qp_examples.md
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Expand Up @@ -123,6 +123,36 @@ if problem.Status.name == "Optimal":
print(f"Objective = {problem.ObjValue:.4f}")
```

## Reading Duals from a QP

A QP with **linear** constraints returns shadow prices and reduced costs just like an LP
(cuOpt's barrier solver is primal-dual). A quadratic *objective* is fine; a quadratic
*constraint* is not — cuOpt returns **no duals for a problem with quadratic constraints**
(every `DualValue`/`ReducedCost` is `NaN`), so read duals only when all constraints are linear.

```python
"""
minimize x² + y² + z²
subject to x + y + z == 10 (linear)
The equality's shadow price is the marginal change in the optimal objective
per unit increase of the right-hand side.
"""
from cuopt.linear_programming.problem import Problem, MINIMIZE

problem = Problem("QPDuals")
x = problem.addVariable(lb=0, name="x")
y = problem.addVariable(lb=0, name="y")
z = problem.addVariable(lb=0, name="z")
problem.setObjective(x*x + y*y + z*z, sense=MINIMIZE)
problem.addConstraint(x + y + z == 10, name="budget")
problem.solve()

if problem.Status.name in ["Optimal", "PrimalFeasible"]:

@mlubin mlubin Jun 9, 2026

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I don't think it's safe or correct to check the dual if the status is PrimalFeasible

@cafzal cafzal Jun 9, 2026

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Resolved.

for c in problem.getConstraints():
# 'budget' dual magnitude ≈ 6.667 (Δobjective per unit of the RHS)
print(f"{c.ConstraintName} DualValue = {c.DualValue}")
```

## Maximization Workaround

```python
Expand Down