# Variable metric method

### From Glossary

Originally referred to the Davidon-Fletcher-Powell (DFP) method, this is a family of methods that choose the direction vector in unconstrained optimization by the subproblem: where is the vector norm (or metric) defined by the quadratic form, With symmetric and positive definite, the constraint restricts d by being on a "circle" -- points that are "equidistant" from a stationary point, called the "center" (the origin in this case). By varying as in the DFP update, to capture the curvature of the objective function, we have a family of ascent algorithms. Besides DFP, if one chooses we have Cauchy's steepest ascent. If is concave and one chooses equal to the negative of the inverse hessian, we have the modified Newton's method.