 Quasi-Newton method

A Quasi-Newton method replaces the Hessian matrix in Newton's method in optimization by a matrix $B_k$ learned from successive gradients. Solving $B_k{s}_k=-\nabla f(x_k)$ gives a descent direction whenever $B_k$ is a positive-definite symmetric matrix and the gradient is nonzero. After choosing a step size, one updates $B_k$ to satisfy the Quasi-Newton secant equation, rather than calculating every second derivative again.