40 citations · 78 across the 21 of their papers we have counts for
21 papers
Semidefinite Implementations of the Proximal Point Algorithm and Consequences for Progressive Decoupling in Optimization
Xudong Li, R. Tyrrell Rockafellar, Defeng Sun
The proximal point algorithm for finding a zero of a maximal monotone mapping is the engine that drives augmented Lagrangian methods and various splitting schemes in convex optimiz…
Maximal monotonicity of piecewise polyhedral mappings
Xudong Li, R. Tyrrell Rockafellar, Defeng Sun
Maximal monotone mappings that are piecewise polyhedral arise from subdifferentials of convex functions and saddle functions that are piecewise linear-quadratic and enter into algo…
A Semismooth Newton Augmented Lagrangian Method for Sparse Spectral Risk Optimization
Rufeng Xiao, Rujun Jiang, Xudong Li +1
Empirical risk minimization is a standard and effective paradigm for learning predictive models by minimizing average loss. In high-stakes decision-making, however, an average-loss…
On the B-subdifferential of proximal operators of affine-constrained regularizer
Xudong Li, Meixia Lin, Kim-Chuan Toh
In this work, we study the affine-constrained regularizers, which frequently arise in statistical and machine learning problems across a variety of applications, including…
An Accelerated Proximal Alternating Direction Method of Multipliers for Optimal Decentralized Control of Uncertain Systems
Bo Yang, Xinyuan Zhao, Xudong Li +1
To ensure the system stability of the -guaranteed cost optimal decentralized control problem (ODC), an approximate semidefinite programming (SDP) problem is f…
An active-set based recursive approach for solving convex isotonic regression with generalized order restrictions
Xuyu Chen, Xudong Li, Yangfeng Su
This paper studies the convex isotonic regression with generalized order restrictions induced by a directed tree. The proposed model covers various intriguing optimization problems…
Solving Stackelberg Prediction Game with Least Squares Loss via Spherically Constrained Least Squares Reformulation
Jiali Wang, Wen Huang, Rujun Jiang +2
The Stackelberg prediction game (SPG) is popular in characterizing strategic interactions between a learner and an attacker. As an important special case, the SPG with least square…
Data-Driven Minimax Optimization with Expectation Constraints
Shuoguang Yang, Xudong Li, Guanghui Lan
Attention to data-driven optimization approaches, including the well-known stochastic gradient descent method, has grown significantly over recent decades, but data-driven constrai…
Fast Algorithms for Stackelberg Prediction Game with Least Squares Loss
Jiali Wang, He Chen, Rujun Jiang +2
The Stackelberg prediction game (SPG) has been extensively used to model the interactions between the learner and data provider in the training process of various machine learning…
QPPAL: A two-phase proximal augmented Lagrangian method for high dimensional convex quadratic programming problems
Ling Liang, Xudong Li, Defeng Sun +1
In this paper, we aim to solve high dimensional convex quadratic programming (QP) problems with a large number of quadratic terms, linear equality and inequality constraints. In or…
A dynamic programming approach for generalized nearly isotonic optimization
Zhensheng Yu, Xuyu Chen, Xudong Li
Shape restricted statistical estimation problems have been extensively studied, with many important practical applications in signal processing, bioinformatics, and machine learnin…
Fast projection onto the ordered weighted norm ball
Qinzhen Li, Xudong Li
In this paper, we provide a finitely terminated yet efficient approach to compute the Euclidean projection onto the ordered weighted (OWL1) norm ball. In particular, an ef…
An asymptotically superlinearly convergent semismooth Newton augmented Lagrangian method for Linear Programming
Xudong Li, Defeng Sun, Kim-Chuan Toh
Powerful interior-point methods (IPM) based commercial solvers, such as Gurobi and Mosek, have been hugely successful in solving large-scale linear programming (LP) problems. The h…
On the Equivalence of Inexact Proximal ALM and ADMM for a Class of Convex Composite Programming
Liang Chen, Xudong Li, Defeng Sun +1
In this paper, we show that for a class of linearly constrained convex composite optimization problems, an (inexact) symmetric Gauss-Seidel based majorized multi-block proximal alt…
On efficiently solving the subproblems of a level-set method for fused lasso problems
Xudong Li, Defeng Sun, Kim-Chuan Toh
In applying the level-set method developed in [Van den Berg and Friedlander, SIAM J. on Scientific Computing, 31 (2008), pp.~890--912 and SIAM J. on Optimization, 21 (2011), pp.~12…
A block symmetric Gauss-Seidel decomposition theorem for convex composite quadratic programming and its applications
Xudong Li, Defeng Sun, Kim-Chuan Toh
For a symmetric positive semidefinite linear system of equations , where is partitioned into blocks, with …
On the efficient computation of a generalized Jacobian of the projector over the Birkhoff polytope
Xudong Li, Defeng Sun, Kim-Chuan Toh
We derive an explicit formula, as well as an efficient procedure, for constructing a generalized Jacobian for the projector of a given square matrix onto the Birkhoff polytope, i.e…
A highly efficient semismooth Newton augmented Lagrangian method for solving Lasso problems
Xudong Li, Defeng Sun, Kim-Chuan Toh
We develop a fast and robust algorithm for solving large scale convex composite optimization models with an emphasis on the -regularized least squares regression (Lasso) pr…
QSDPNAL: A two-phase augmented Lagrangian method for convex quadratic semidefinite programming
Xudong Li, Defeng Sun, Kim-Chuan Toh
In this paper, we present a two-phase augmented Lagrangian method, called QSDPNAL, for solving convex quadratic semidefinite programming (QSDP) problems with constraints consisting…
On the convergence properties of a majorized ADMM for linearly constrained convex optimization problems with coupled objective functions
Ying Cui, Xudong Li, Defeng Sun +1
In this paper, we establish the convergence properties for a majorized alternating direction method of multipliers (ADMM) for linearly constrained convex optimization problems whos…
A Schur Complement Based Semi-Proximal ADMM for Convex Quadratic Conic Programming and Extensions
Xudong Li, Defeng Sun, Kim-Chuan Toh
This paper is devoted to the design of an efficient and convergent {semi-proximal} alternating direction method of multipliers (ADMM) for finding a solution of low to medium accura…