# Optimization Algorithms

## Gradient Descent Algorithm and Its Variants

Trajectory towards local minimum. Optimization refers to the task of minimizing/maximizing an objective function f(x) parameterized by x. In machine/deep learning terminology, it’s the task of minimizing the cost/loss function J(w) parameterized by the model’s parameters $w \in \mathbb{R}^d$. Optimization algorithms (in case of minimization) have one of the following goals: Find the global minimum of the objective function. This is feasible if the objective function is convex, i.