Accelerated gradient methods for nonconvex nonlinear and stochastic programming

In this paper, we generalize the well-known Nesterov’s accelerated gradient (AG) method, originally designed for convex smooth optimization, to solve nonconvex and possibly stochastic optimization problems. We demonstrate that by properly specifying the stepsize policy, the AG method exhibits the best known rate of convergence for solving general nonconvex smooth optimization problems by using first-order information, similarly to the gradient descent method. We then consider an important class of composite optimization problems and show that the AG method can solve them uniformly, i.e., by using the same aggressive stepsize policy as in the convex case, even if the problem turns out to be nonconvex. More specifically, the AG method exhibits an optimal rate of convergence if the composite problem is convex, and improves the best known rate of convergence if the problem is nonconvex. Based on the AG method, we also present new nonconvex stochastic approximation methods and show that...

• Type: Journal
• Year: 2016
• Where: MP
• Authors: Saeed Ghadimi, Guanghui Lan
• Keywords: Information Technology, MP 2016