フェンシェルの双対性定理
f ⋆ ( x ∗ ) := sup { ⟨ x ∗ , x ⟩ − f ( x ) | x ∈ R n } {\displaystyle f^{\star }\left(x^{*}\right):=\sup \left\{\left.\left\langle x^{*},x\right\rangle -f\left(x\right)\right|x\in \mathbb {R} ^{n}\right\}}
g ⋆ ( x ∗ ) := inf { ⟨ x ∗ , x ⟩ − g ( x ) | x ∈ R n } {\displaystyle g_{\star }\left(x^{*}\right):=\inf \left\{\left.\left\langle x^{*},x\right\rangle -g\left(x\right)\right|x\in \mathbb {R} ^{n}\right\}}