7 papers · 1 filter
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…