Inspect the boundary of a scalar optimization result

Define the task

Write the objective function and identify whether it represents a cost to minimize or a benefit requiring a sign change. Define the feasible interval using the actual scientific or operational constraint. An unconstrained solution outside the allowed region cannot simply be treated as an admissible optimum.

Carry out the check

Use a bounded method when the interval is part of the problem. Check the returned status, objective value and proximity to both bounds. Evaluate endpoints separately where the application permits them. A boundary result may indicate a constraint-limited solution. Multiple local minima require additional investigation because a scalar local search does not certify a global optimum for an arbitrary function.

Worked hypothetical example

For hypothetical cost (x−3)² on the interval from 0 to 2, the unconstrained minimum is at 3, while the constrained minimum is at the upper endpoint 2 with cost 1. A reported value near 2 should be interpreted with the solver tolerance and endpoint check. Record the interval, method, stopping criteria and objective evaluations so another analyst can distinguish numerical termination from a substantive optimum.

Method checked 14 November 2026 against SciPy documentation: minimize_scalar.