A Lipschitz Method for Accelerated

An effective optimization algorithm for locally nonconvex Lipschitz functions based on mollifier subgradients

An Accelerated Hybrid Proximal Extragradient Method for Convex Optimization and Its Implications to Second-Order Methods

This paper presents an accelerated variant of the hybrid proximal extragradient (HPE) method for convex optimization, referred to as the accelerated HPE (A-HPE) framework. Iterationcomplexity results are established for the A-HPE framework, as well as a special version of it, where a large stepsize condition is imposed. Two specific implementations of the A-HPE framework are described in the co...

Accelerated Mirror Descent in Continuous and Discrete Time

We study accelerated mirror descent dynamics in continuous and discrete time. Combining the original continuous-time motivation of mirror descent with a recent ODE interpretation of Nesterov’s accelerated method, we propose a family of continuous-time descent dynamics for convex functions with Lipschitz gradients, such that the solution trajectories converge to the optimum at a O(1/t2) rate. We...

Accelerated gradient sliding for structured convex optimization

Our main goal in this paper is to show that one can skip gradient computations for gradient descent type methods applied to certain structured convex programming (CP) problems. To this end, we first present an accelerated gradient sliding (AGS) method for minimizing the summation of two smooth convex functions with different Lipschitz constants. We show that the AGS method can skip the gradient...

Accelerated Methods for Non-Convex Optimization

We present an accelerated gradient method for non-convex optimization problems with Lipschitz continuous first and second derivatives. The method requires time O( −7/4 log(1/ )) to find an -stationary point, meaning a point x such that ‖∇f(x)‖ ≤ . The method improves upon the O( −2) complexity of gradient descent and provides the additional second-order guarantee that ∇f(x) −O( )I for the compu...