Consider the minimization problem \(\displaystyle \min _{x\in {\mathbb R}^n} f(x), \) where \(f: {\mathbb R}^n \to (-\infty, \infty]\) is a proper convex function. In case f is continuous differentiable everywhere, the gradient method solves (3.1) iteratively by using the gradient of f to produce a sequence toward a minimizer.