In this paper, we study the convergence rate of the gradient (or steepest descent) method with fixed step lengths for finding a stationary point of an L-smooth function. We establish a new convergence rate, and show that the bound may be exact in some cases, in particular when all step lengths lie in the interval (0,1/L]. In addition, we derive an optimal step length with respect to the new bound.
- l-smooth optimization
- gradient method
- performance estomation prolem
- semidefinite programming