Davidon–Fletcher–Powell formula

The Davidon–Fletcher–Powell formula (or DFP; named after William C. Davidon, Roger Fletcher, and Michael J. D. Powell) finds the solution to the secant equation that is closest to the current estimate and satisfies the curvature condition (see below). It was the first quasi-Newton method to generalize the secant method to a multidimensional problem. This update maintains the symmetry and positive definiteness of the Hessian matrix.

Given a function ${\displaystyle f(x)}$, its gradient (${\displaystyle \nabla f}$), and positive definite Hessian matrix ${\displaystyle B}$, the Taylor series is:

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