13 papers
Standard Transformers Achieve the Minimax Rate in Nonparametric Regression with Targets
Yanming Lai, Defeng Sun
The tremendous success of Transformer models in fields such as large language models and computer vision necessitates a rigorous theoretical investigation. To the best of our knowl…
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…
On the -order Semismoothness of the Metric Projection onto Slices of the Positive Semidefinite Cone
Ruoning Chen, Jiaming Ma, Defeng Sun
The metric projection onto the positive semidefinite (PSD) cone is strongly semismooth, a property that guarantees local quadratic convergence for many powerful algorithms in semid…
The Aubin Property for Generalized Equations over -cone Reducible Sets
Jiaming Ma, Defeng Sun
This paper establishes the equivalence between the Aubin property and strong regularity for generalized equations over -cone reducible sets. This result resolves a long-standi…
Complexity of normalized stochastic first-order methods with momentum under heavy-tailed noise
Chuan He, Zhaosong Lu, Defeng Sun +1
In this paper, we propose practical normalized stochastic first-order methods with Polyak momentum, multi-extrapolated momentum, and recursive momentum for solving unconstrained op…
Support matrix machine: exploring sample sparsity, low rank, and adaptive sieving in high-performance computing
Can Wu, Dong-Hui Li, Defeng Sun
Support matrix machine (SMM) is a successful supervised classification model for matrix-type samples. Unlike support vector machines, it employs low-rank regularization on the regr…
Robust Gradient Descent Estimation for Tensor Models under Heavy-Tailed Distributions
Xiaoyu Zhang, Di Wang, Guodong Li +1
Low-rank tensor models are widely used in statistics. However, most existing methods rely heavily on the assumption that data follows a sub-Gaussian distribution. To address the ch…
Lipschitz stability of least-squares problems regularized by functions with -cone reducible conjugates
Ying Cui, Tim Hoheisel, Tran T. A. Nghia +1
In this paper, we study Lipschitz continuity of the solution mappings of regularized least-squares problems for which the convex regularizers have (Fenchel) conjugates that are $\m…
Characterizations of the Aubin Property of the Solution Mapping for Nonlinear Semidefinite Programming
Liang Chen, Ruoning Chen, Defeng Sun +1
In this paper, we study the Aubin property of the Karush-Kuhn-Tucker solution mapping for the nonlinear semidefinite programming (NLSDP) problem at a locally optimal solution. In t…
Two Typical Implementable Semismooth* Newton Methods for Generalized Equations are G-Semismooth Newton Methods
Liang Chen, Defeng Sun, Wangyongquan Zhang
Semismooth* Newton methods have been proposed in recent years targeting multi-valued inclusion problems and have been successfully implemented to deal with several concrete general…
Aubin Property and Strong Regularity Are Equivalent for Nonlinear Second-Order Cone Programming
Liang Chen, Ruoning Chen, Defeng Sun +1
This paper solves a fundamental open problem in variational analysis on the equivalence between the Aubin property and the strong regularity for nonlinear second-order cone program…
Machine Learning Insides OptVerse AI Solver: Design Principles and Applications
Xijun Li, Fangzhou Zhu, Hui-Ling Zhen +23
In an era of digital ubiquity, efficient resource management and decision-making are paramount across numerous industries. To this end, we present a comprehensive study on the inte…
Solving polynomial variational inequality problems via Lagrange multiplier expressions and Moment-SOS relaxations
Jiawang Nie, Defeng Sun, Xindong Tang +1
In this paper, we study variational inequality problems (VIPs) with involved mappings and feasible sets characterized by polynomial functions (namely, polynomial VIPs). We propose…