descent direction

At a point x with \nabla f(x)\ne\mathbf 0, a direction d is a descent direction if \nabla f(x)^\top d < 0 — the directional derivative of f along d is negative, so f(x+\alpha d)<f(x) for all sufficiently small \alpha>0. Every first-order descent method (gradient descent, Newton's method, conjugate gradient, and more) is an instance of picking some descent direction, then a step size, at every iteration.