cuopt-numerical-optimization-formulation

# Numerical Optimization Formulation Concepts and workflow for going from a problem description to a clear formulation across LP, MILP, and QP. No API code here. ## What is LP / MILP / QP - **LP**: Linear objective, linear constraints, continuous variables. - **MILP**: Same as LP plus some integer or binary variables (e.g., scheduling, facility location, selection). - **QP**: Quadratic objective (e.g., x², x·y terms — portfolio variance, least squares), linear constraints. **QP support in cuOpt is currently in beta.** ## Identifying problem type | Property | LP | MILP | QP | |---|---|---|---| | Objective | Linear | Linear | Quadratic (xᵀQx + cᵀx) | | 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 | 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** (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 mu...