Skip to content

Correct quadratic-constraint claims in formulation skill #1407

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
cafzal wants to merge 3 commits into
base: main
Choose a base branch
from
+4 −4
Open

Correct quadratic-constraint claims in formulation skill #1407

Changes from all commits
Commits
Show all changes
3 commits
Select commit Hold shift + click to select a range
8904e35
Correct quadratic-constraint claims in formulation skill
cafzal Jun 8, 2026
0f44091
Address review: drop "PSD" from quadratic-constraint wording
cafzal Jun 9, 2026
1048880
Align dual wording with #1408 review: drop "shadow prices"
cafzal Jun 9, 2026
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
8 changes: 4 additions & 4 deletions skills/cuopt-numerical-optimization-formulation/SKILL.md
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -29,22 +29,22 @@ Concepts and workflow for going from a problem description to a clear formulatio
| Property | LP | MILP | QP |
|---|---|---|---|
| Objective | Linear | Linear | Quadratic (xᵀQx + cᵀx) |
| Constraints | Linear | Linear | Linear (no quadratic constraints) |
| Constraints | Linear | Linear | Linear + convex quadratic (inequality only) via second-order cones |
| Variables | Continuous | Mixed: continuous + integer/binary | Continuous |
| Sense | min or max | min or max | **minimize only** (negate to max) |
| Duals / sensitivity | Shadow prices + reduced costs | **None** (integer optima) | Shadow prices + reduced costs |
| Duals / sensitivity | Dual values + reduced costs | **None** (integer optima) | Dual values + reduced costs |

If the objective is purely linear, prefer LP/MILP — do not artificially introduce quadratic terms. If any variable is integer or binary, the problem is MILP regardless of the rest.

**Post-solve sensitivity (LP / QP only).** Continuous LP and QP solutions expose **dual values** (shadow prices — the marginal objective change per unit a binding constraint is relaxed: *where to invest to improve the outcome*) and **reduced costs** (for a variable the optimizer left at zero, how far it must improve to enter the solution: a *near-miss*). **MILP solutions have no duals** — integer optima are not continuous, so there are none to return. See the language-specific API skills for how to retrieve them after a solve.
**Post-solve sensitivity (LP / QP only).** Continuous LP and QP solutions expose **dual values** (the marginal objective change per unit a binding constraint is relaxed: *where to invest to improve the outcome*) and **reduced costs** (for a variable the optimizer left at zero, how far it must improve to enter the solution: a *near-miss*). **MILP solutions have no duals** — integer optima are not continuous, so there are none to return. Duals are also unavailable when the model includes quadratic constraints — the second-order cone path returns primal values only. See the language-specific API skills for how to retrieve them after a solve.

## Required formulation questions

Ask these if not already clear:

1. **Decision variables** — What are they? Bounds?
2. **Objective** — Minimize or maximize? Linear or quadratic? For QP: any squared or cross terms (x², x·y)? If maximize a quadratic, the user must negate and minimize.
3. **Constraints** — Linear inequalities/equalities? (Quadratic constraints are not supported.)
3. **Constraints** — Linear inequalities/equalities? Convex quadratic constraints (inequality only) are also supported, handled as second-order cones; non-convex or equality quadratic constraints are not.
4. **Variable types** — All continuous (LP / QP) or some integer/binary (MILP)?
5. **Convexity (QP only)** — For minimization, the quadratic form (matrix Q) should be positive semi-definite for well-posed problems.

Expand Down