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# Gradient Descent

Simply use gradient information.

Let's say you have function $$f(x)$$ that you want to mimimize. 

With gradient descent to just iterate to move $$x$$ in the negative of the gradient i.e $$-f'(x)$$. Hence at each step, we take one gradient step as below

$$
\mathbf x\_{t+1} = \mathbf x\_{t} - \alpha f'(\mathbf x)
$$

Here $$\alpha$$is the step size, determines how big do we want to move in the direction of negative of gradient $$f'(\mathbf x )$$. 

**The above equation basically represents a eqn of line in vector form. Where the line start passes** $$\mathbf x\_t$$ **in the direction of vector** $$f'(\mathbf x)$$**. For all the values of** $$\alpha$$**, you will be able to get all the points that lies on that line.**