Quasi-Newton method
= Quasi-Newton method
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A <Quasi-Newton method> replaces the <Hessian matrix> in <Newton's method in optimization> by a <matrix> $B_k$ learned from successive <gradients>. Solving $B_ks_k=-\nabla f(x_k)$ 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.