duality_arguments

To prove primal problems via duality in Lean 4, transform them into dual problems and exploit weak or strong duality to transfer bounds. The Skill provides Lean 4 templates and Mathlib references for formal duality proofs.

Weak and strong duality in optimization theory bound primal and dual problems. Weak duality provides dual bounds, while strong duality ensures matching optimal values, enabling dual certificates to prove min-max theorems and optimality conditions.

Generate a dual certificate for a linear programming problem by applying duality transformations to derive bounds. The Skill provides illustrative LP examples demonstrating how to extract dual certificates and prove optimality.

Yes, you can apply duality arguments to combinatorial optimization and game theory proofs. The Skill demonstrates translating these problems into duals to derive dual certificates and prove min-max theorems.

Using Lean 4 duality proof templates requires Mathlib references to support formal proofs. The Skill delivers templates relying on Mathlib's mathematical groundwork to construct dual certificates and verify optimality conditions.