CMP.6:4.5 - Choose a stopping test that supports the receiving answer

Derive the test from the wanted conclusion. Exhausting a discrete neighborhood establishes local optimality for that neighborhood. A residual threshold answers a residual question; a condition or error bound is needed to convert it into distance from a solution. Small successive changes can result from a tiny step even while the candidate remains poor.

For a constrained optimum, the full gradient need not vanish. Use the absence of a feasible improving variation, a suitable projected update or the relevant constrained condition. Report that condition at the scope it establishes.

When time runs out, return the best admissible candidate or current approximation together with any supported bound. A tolerance or resource limit belongs to the use that needs the result.