Descent methods

Descent methods are a set of methods to iteratively minimize a function $$f(x)$$. Following is the general outline of descent methods: $$\textbf{given} \text{ a starting point } x \in \textbf{dom}f \\ \textbf{repeat} \\ \text{ 1. Determine a descent direction }\Delta x\\ \text{ 2. Line search. Choose a step step size} t>0\\ \text{3. Update}. x = x+t\Delta x \\ \textbf{until } stopping criterion satisfied $$