7 papers
Progressive Bound Strengthening via Doubly Nonnegative Cutting Planes for Nonconvex Quadratic Programs
Zheng Qu, Defeng Sun, Jintao Xu
We introduce a cutting-plane framework for nonconvex quadratic programs (QPs) that progressively tightens convex relaxations. Our approach leverages the doubly nonnegative (DNN) re…
Stochastic versus Deterministic in Stochastic Gradient Descent
Runze Li, Jintao Xu, Wenxun Xing
This paper theoretically reanalyzes the convergence of the mini-batch stochastic gradient descent (SGD) for a structured minimization problem involving a finite-sum function with i…
A Regularized Newton Method for Nonconvex Optimization with Global and Local Complexity Guarantees
Yuhao Zhou, Jintao Xu, Bingrui Li +3
Finding an -stationary point of a nonconvex function with a Lipschitz continuous Hessian is a central problem in optimization. Regularized Newton methods are a classical tool an…
Stable gradient-adjusted root mean square propagation on least squares problem
Runze Li, Jintao Xu, Wenxun Xing
Root mean square propagation (abbreviated as RMSProp) is a first-order stochastic algorithm used in machine learning widely. In this paper, a stable gradient-adjusted RMSProp (abbr…
Semidefinite Programming Approximation for a Matrix Optimization Problem over an Uncertain Linear System
Jintao Xu, Shu-Cherng Fang, Wenxun Xing
A matrix optimization problem over an uncertain linear system on finite horizon (abbreviated as MOPUL) is studied, in which the uncertain transition matrix is regarded as a decisio…
ADMM Algorithms for Residual Network Training: Convergence Analysis and Parallel Implementation
Jintao Xu, Yifei Li, Wenxun Xing
We propose both serial and parallel proximal (linearized) alternating direction method of multipliers (ADMM) algorithms for training residual neural networks. In contrast to backpr…
Convergence Rates of Training Deep Neural Networks via Alternating Minimization Methods
Jintao Xu, Chenglong Bao, Wenxun Xing
Training deep neural networks (DNNs) is an important and challenging optimization problem in machine learning due to its non-convexity and non-separable structure. The alternating…