カルーシュ・クーン・タッカー条件
For maximizing f(x): ∇ f ( x ∗ ) = ∑ i = 1 m μ i ∇ g i ( x ∗ ) + ∑ j = 1 l λ j ∇ h j ( x ∗ ) , {\displaystyle \nabla f(x^{*})=\sum _{i=1}^{m}\mu _{i}\nabla g_{i}(x^{*})+\sum _{j=1}^{l}\lambda _{j}\nabla h_{j}(x^{*}),}
For minimizing f(x): − ∇ f ( x ∗ ) = ∑ i = 1 m μ i ∇ g i ( x ∗ ) + ∑ j = 1 l λ j ∇ h j ( x ∗ ) , {\displaystyle -\nabla f(x^{*})=\sum _{i=1}^{m}\mu _{i}\nabla g_{i}(x^{*})+\sum _{j=1}^{l}\lambda _{j}\nabla h_{j}(x^{*}),}