Lagrange-Funktion

Lagrange-Multiplikatoren

L(x,λ,μ):=f(x)+j=1mλjhj(x)+i=1μigi(x)\mathcal{L}(x, \lambda, \mu):=f(x)+\sum_{j=1}^{m} \lambda_{j} h_{j}(x)+\sum_{i=1}^{\ell} \mu_{i} g_{i}(x)

Hessematrix

xx2L(x,λ,μ)=2f(x)+j=1mλj2hj(x)+i=1lμi2gi(x)\nabla_{x x}^{2} \mathcal{L}(x, \lambda, \mu)=\nabla^{2} f(x)+\sum_{j=1}^{m} \lambda_{j} \nabla^{2} h_{j}(x)+\sum_{i=1}^{l} \mu_{i} \nabla^{2} g_{i}(x)