Why is the gradient descent of this problem with an extremely small step size (start at $\mathbf{x_0}=\mathbf{0}$) $$ \min_\mathbf{x} ||\mathbf{y}-\mathbf{A}\mathbf{x}||_2^2 $$ equivalent to $$ \min_\mathbf{x} ||\mathbf{x}||_2^2 s.t. \mathbf{y}=\mathbf{A}\mathbf{x} $$ where $\mathbf{x}$ and $\mathbf{y}$ are vectors and $\mathbf{A}$ is a fat matrix.
It seems to be a common result but I cannot tell the why, could anyone help me with that?