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Fixed infinity problem.

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Bokuan Li
2026-06-25 12:23:40 -04:00
parent d857ff2bb7
commit c19aaf7fe3
1 changed files with 1 additions and 1 deletions
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src/fa/convex/legendre.tex
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@@ -195,7 +195,7 @@
Since for any $(y, \beta) \in A$, $\beta$ may be arbitrarily large by \autoref{lemma:closed-convex-epigraph}, $\mu \le 0$. Since for any $(y, \beta) \in A$, $\beta$ may be arbitrarily large by \autoref{lemma:closed-convex-epigraph}, $\mu \le 0$.
In the case that $\mu < 0$, for each $y \in E$, In the case that $\mu < 0$, for each $y \in \bracs{f < \infty}$,
\begin{align*} \begin{align*}
\dpn{x, \phi}{\lambda} + \mu\alpha &> \dpn{y, \phi}{\lambda} + \mu f(y) \\ \dpn{x, \phi}{\lambda} + \mu\alpha &> \dpn{y, \phi}{\lambda} + \mu f(y) \\
\dpn{x, \mu^{-1}\phi}{\lambda} + \alpha & < \dpn{y, \mu^{-1}\phi}{\lambda} + f(y) \\ \dpn{x, \mu^{-1}\phi}{\lambda} + \alpha & < \dpn{y, \mu^{-1}\phi}{\lambda} + f(y) \\