Newton decrement

lambda^2 / 2 estimates f(x) - p* and is affine-invariant, unlike the gradient norm – which is why it is the standard stopping rule for Newton's method.

Usage

morie_boyd_newton_decrement(grad, hess)

Arguments

grad

Gradient, length n.

hess

Hessian, n-by-n, symmetric positive definite.

Value

List with decrement, suboptimality, grad_norm.

References

Boyd, S., & Vandenberghe, L. (2004). Convex Optimization, Sec 9.5.1.

Examples

A <- matrix(c(4, 1, 1, 3), 2)
x <- c(5, -2)
morie_boyd_newton_decrement(A %*% x, A)$suboptimality
#> [1] 46