= Monotonicity of a constrained minimum under added constraints
{title2=$A\subseteq B\Longrightarrow\inf_A f\geq\inf_B f$}
Adding an <optimization constraint> shrinks the admissible set, so it cannot lower the infimum of the same <objective function>. Every value attained on the smaller set was already available on the larger set. If both minima exist and the larger problem has a unique minimizer absent from the smaller set, the inequality is strict. This compares beam energies for free, pinned, and clamped endpoints without evaluating the energy integrals.
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