Concept

BFGS Methodis a secant updating methods of quasi-Newton’s method.
take 𝐵0=𝐼 or initial guess of 𝐻.

solve 𝐵𝑘𝑠𝑘=𝑓(𝑥𝑘)
𝑥{𝑘+1}=𝑥𝑘+𝑠𝑘
𝑦𝑘=𝑓(𝑥𝑘+1)𝑓(𝑥𝑘)

𝐵𝑘+1=𝐵𝑘+𝑦𝑘𝑦𝑇𝑘𝑦𝑇𝑘𝑠𝑘𝐵𝑘𝑠𝑘𝑠𝑇𝑘𝐵𝑘𝑠𝑇𝑘𝐵𝑘𝑠𝑘

repeat this.