4 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…