Accelerated gradient methods for nonconvex optimization: Escape trajectories from strict saddle points and convergence to local minima

no code implementations • 13 Jul 2023 • Rishabh Dixit, Mert Gurbuzbalaban, Waheed U. Bajwa

This work also develops two metrics of asymptotic rate of convergence and divergence, and evaluates these two metrics for several popular standard accelerated methods such as the NAG, and Nesterov's accelerated gradient with constant momentum (NCM) near strict saddle points.

Boundary Conditions for Linear Exit Time Gradient Trajectories Around Saddle Points: Analysis and Algorithm

no code implementations • 7 Jan 2021 • Rishabh Dixit, Mert Gurbuzbalaban, Waheed U. Bajwa

This paper concerns convergence of first-order discrete methods to a local minimum of nonconvex optimization problems that comprise strict-saddle points within the geometrical landscape.

Exit Time Analysis for Approximations of Gradient Descent Trajectories Around Saddle Points

no code implementations • 1 Jun 2020 • Rishabh Dixit, Mert Gurbuzbalaban, Waheed U. Bajwa

This paper considers the problem of understanding the exit time for trajectories of gradient-related first-order methods from saddle neighborhoods under some initial boundary conditions.

Online Learning over Dynamic Graphs via Distributed Proximal Gradient Algorithm

no code implementations • 16 May 2019 • Rishabh Dixit, Amrit Singh Bedi, Ketan Rajawat

The empirical performance of the proposed algorithm is tested on the distributed dynamic sparse recovery problem, where it is shown to incur a dynamic regret that is close to that of the centralized algorithm.