128 citations · 505 across the 21 of their papers we have counts for
9 papers · 1 filter
A Single-Loop Gradient Descent and Perturbed Ascent Algorithm for Nonconvex Functional Constrained Optimization
Songtao Lu
Nonconvex constrained optimization problems can be used to model a number of machine learning problems, such as multi-class Neyman-Pearson classification and constrained Markov dec…
Rate-improved Inexact Augmented Lagrangian Method for Constrained Nonconvex Optimization
Zichong Li, Pin-Yu Chen, Sijia Liu +2
First-order methods have been studied for nonlinear constrained optimization within the framework of the augmented Lagrangian method (ALM) or penalty method. We propose an improved…
Randomized Bregman Coordinate Descent Methods for Non-Lipschitz Optimization
Tianxiang Gao, Songtao Lu, Jia Liu +1
We propose a new \textit{randomized Bregman (block) coordinate descent} (RBCD) method for minimizing a composite problem, where the objective function could be either convex or non…
Leveraging Two Reference Functions in Block Bregman Proximal Gradient Descent for Non-convex and Non-Lipschitz Problems
Tianxiang Gao, Songtao Lu, Jia Liu +1
In the applications of signal processing and data analytics, there is a wide class of non-convex problems whose objective function is freed from the common global Lipschitz continu…
Improving the Sample and Communication Complexity for Decentralized Non-Convex Optimization: A Joint Gradient Estimation and Tracking Approach
Haoran Sun, Songtao Lu, Mingyi Hong
Many modern large-scale machine learning problems benefit from decentralized and stochastic optimization. Recent works have shown that utilizing both decentralized computing and lo…
SNAP: Finding Approximate Second-Order Stationary Solutions Efficiently for Non-convex Linearly Constrained Problems
Songtao Lu, Meisam Razaviyayn, Bo Yang +2
This paper proposes low-complexity algorithms for finding approximate second-order stationary points (SOSPs) of problems with smooth non-convex objective and linear constraints. Wh…
Hybrid Block Successive Approximation for One-Sided Non-Convex Min-Max Problems: Algorithms and Applications
Songtao Lu, Ioannis Tsaknakis, Mingyi Hong +1
The min-max problem, also known as the saddle point problem, is a class of optimization problems which minimizes and maximizes two subsets of variables simultaneously. This class o…
On the Sublinear Convergence of Randomly Perturbed Alternating Gradient Descent to Second Order Stationary Solutions
Songtao Lu, Mingyi Hong, Zhengdao Wang
The alternating gradient descent (AGD) is a simple but popular algorithm which has been applied to problems in optimization, machine learning, data ming, and signal processing, etc…
A Nonconvex Splitting Method for Symmetric Nonnegative Matrix Factorization: Convergence Analysis and Optimality
Songtao Lu, Mingyi Hong, Zhengdao Wang
Symmetric nonnegative matrix factorization (SymNMF) has important applications in data analytics problems such as document clustering, community detection and image segmentation. I…