Let $X$ be a reflexive [Banach space](/page/Banach%20Space) with norm $\|\cdot\|_X$, let $\mathcal A \subset X$ be sequentially weakly closed, and let
paragraph
admin
\begin{align*}
I:\mathcal A \to (-\infty,\infty]
\end{align*}
latex_env
admin
be sequentially weakly lower semicontinuous. Assume that $I$ is coercive on $\mathcal A$, in the sense that for every $M\in\mathbb R$ there exists $R_M>0$ such that if $u\in\mathcal A$ and $I[u]\le M$, then