Lax Lean Archive

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Proof of `Improving directions certify unboundedness`

groundedproofs/Lax109476Proofs/Certificates.lean · lax-109476

What this proof establishes

no assumptions

thm✓Lax109476.RecessionSoundness

Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.

Read the Lean proof on GitHub

Description

Given a proposed bound BB, move from the feasible base point along the improving direction by (B−cTx)/(cTd)+1(B-c^T x)/(c^T d)+1. This nonnegative step preserves feasibility and gives objective B+cTd>BB+c^T d>B.