Let $X$ be a [Banach space](/page/Banach%20Space), let $\mathcal A \subset X$, and let $I:\mathcal A\to(-\infty,\infty]$ be coercive in the following sequential sense: whenever $(v_k)_{k=1}^{\infty}$ is a sequence in $\mathcal A$ with $\|v_k\|_X\to\infty$, one has $I[v_k]\to+\infty$. Assume that