Talk:Fenchel's duality theorem

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Negation Notation[edit]

In Section "Mathematical theorem", why the unwieldy notation with negated functions

p^{*}=\inf _{x\in X}\{f(x)+g(Ax)\}

d^{*}=\sup _{y^{*}\in Y^{*}}\{-f^{*}(A^{*}y^{*})-g^{*}(-y^{*})\}

instead of

p^{*}=\inf _{x\in X}\{f(x)+g(Ax)\}

d^{*}=\inf _{y^{*}\in Y^{*}}\{f^{*}(A^{*}y^{*})+g^{*}(-y^{*})\}

? — Preceding unsigned comment added by 132.185.132.13 (talk) 10:12, 29 April 2014 (UTC)[reply]

Answering my own (stupid) question: Because $\sup _{y^{*}\in Y^{*}}\{-f^{*}(A^{*}y^{*})-g^{*}(-y^{*})\}=-\inf _{y^{*}\in Y^{*}}\{f^{*}(A^{*}y^{*})+g^{*}(-y^{*})\}$ which is equally unwieldy. — Preceding unsigned comment added by 132.185.132.13 (talk) 11:08, 29 April 2014 (UTC)[reply]

Sup Notation[edit]

Is there a reason "max" rather than "sup" is used in the lede? Jess_Riedel (talk) 03:07, 2 July 2017 (UTC)[reply]

Thanks for noticing that. It was left over from a much earlier version which had min/max. Encyclops (talk) 18:28, 3 July 2017 (UTC)[reply]