Concept

ℒ︀(𝑥,𝜆)=𝑓(𝑥)+𝜆𝑇𝑔(𝑥)

where 𝜆 is vector of Lagrangian multipliers, 𝑔 is constrains function, and

ℒ︀(𝑥,𝜆)=[𝑓(𝑥)+𝐽𝑇𝑔𝜆𝑔(𝑥)]

where 𝐽 is Jacobian matrix.

𝐻ℒ︀(𝑥,𝜆)=[𝐵(𝑥,𝜆)𝐽𝑔(𝑥)𝐽𝑇𝑔(𝑥)𝑂]

where 𝑂 is a matrix with zeros and

𝐵(𝑥,𝜆)=𝐻𝑓(𝑥)+𝑚𝑖=1𝜆𝑖𝐻𝑔𝑖(𝑥)

where 𝐻 is Hessian matrix.