CMP.5:4.5 - Return to the original problem and choose the next move

Return the recovered candidate under its original conditions and the bound that applies to the original objective. For minimization, an additive gap C-L bounds how much the candidate can still improve. A ratio uses additional conditions, such as a positive denominator; a zero or negative lower bound does not support a generic ratio claim.

Use the result to adopt the candidate, stop at an adequate gap, guide a branch of CMP.4, tighten the relaxation, revise recovery or choose a different algorithm. The stronger relaxation is worthwhile only if its expected contribution warrants the extra work.

When the question or allowed operations change, recheck the representation i, bound direction and recovery. A bound from a more restrictive former problem may cease to constrain the new one. A bound that remains valid may also become too weak to be useful.