109 citations · 565 across the 64 of their papers we have counts for
59 papers · 1 filter
Solution Set Dimensions in Convex Optimization and Primal-Polar Facial Signatures
Jiaming Ma, Defeng Sun
We study the possible dimensions of solution sets in linearly perturbed convex optimization problems and their behavior under convex duality. The dimensions of solution sets and in…
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…
A symmetric Gauss-Seidel based alternating proximal ALM for generalized Nash Equilibrium problems in Banach spaces
Defeng Sun, Hailing Wang, Wei Zhao
In this paper, we study a class of monotone generalized Nash equilibrium problems (GNEPs) with jointly linear constraints. The players' strategy spaces are real Hilbert spaces, whi…
A Level Set Method with Secant Iterations for the Least-Squares Constrained Nuclear Norm Minimization
Chiyu Ma, Jiaming Ma, Defeng Sun
We present an efficient algorithm for least-squares constrained nuclear norm minimization, a computationally challenging problem with broad applications. Our approach combines a le…
An efficient sieving based secant method for sparse optimization problems with least-squares constraints
Qian Li, Defeng Sun, Yancheng Yuan
In this paper, we propose an efficient sieving based secant method to address the computational challenges of solving sparse optimization problems with least-squares constraints. A…
Quantifying low rank approximations of third order symmetric tensors
Shenglong Hu, Defeng Sun, Kim-Chuan Toh
In this paper, we present a method to certify the approximation quality of a low rank tensor to a given third order symmetric tensor. Under mild assumptions, best low rank approxim…
A Highly Efficient Algorithm for Solving Exclusive Lasso Problems
Meixia Lin, Yancheng Yuan, Defeng Sun +1
The exclusive lasso (also known as elitist lasso) regularizer has become popular recently due to its superior performance on intra-group feature selection. Its complex nature poses…
Adaptive sieving: A dimension reduction technique for sparse optimization problems
Yancheng Yuan, Meixia Lin, Defeng Sun +1
In this paper, we propose an adaptive sieving (AS) strategy for solving general sparse machine learning models by effectively exploring the intrinsic sparsity of the solutions, whe…
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…
A squared smoothing Newton method for semidefinite programming
Ling Liang, Defeng Sun, Kim-Chuan Toh
This paper proposes a squared smoothing Newton method via the Huber smoothing function for solving semidefinite programming problems (SDPs). We first study the fundamental properti…
An Efficient HPR Algorithm for the Wasserstein Barycenter Problem with Computational Complexity
Guojun Zhang, Yancheng Yuan, Defeng Sun
In this paper, we propose and analyze an efficient Halpern-Peaceman-Rachford (HPR) algorithm for solving the Wasserstein barycenter problem (WBP) with fixed supports. While the Pea…
A Dimension Reduction Technique for Large-scale Structured Sparse Optimization Problems with Application to Convex Clustering
Yancheng Yuan, Tsung-Hui Chang, Defeng Sun +1
In this paper, we propose a novel adaptive sieving (AS) technique and an enhanced AS (EAS) technique, which are solver independent and could accelerate optimization algorithms for…
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…
An augmented Lagrangian method with constraint generation for shape-constrained convex regression problems
Meixia Lin, Defeng Sun, Kim-Chuan Toh
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity…
An Inexact Augmented Lagrangian Method for Second-order Cone Programming with Applications
Ling Liang, Defeng Sun, Kim-Chuan Toh
In this paper, we adopt the augmented Lagrangian method (ALM) to solve convex quadratic second-order cone programming problems (SOCPs). Fruitful results on the efficiency of the AL…
Adaptive Sieving with PPDNA: Generating Solution Paths of Exclusive Lasso Models
Meixia Lin, Yancheng Yuan, Defeng Sun +1
The exclusive lasso (also known as elitist lasso) regularization has become popular recently due to its superior performance on structured sparsity. Its complex nature poses diffic…
On Degenerate Doubly Nonnegative Projection Problems
Ying Cui, Ling Liang, Defeng Sun +1
The doubly nonnegative (DNN) cone, being the set of all positive semidefinite matrices whose elements are nonnegative, is a popular approximation of the computationally intractable…
Estimation of sparse Gaussian graphical models with hidden clustering structure
Meixia Lin, Defeng Sun, Kim-Chuan Toh +1
Estimation of Gaussian graphical models is important in natural science when modeling the statistical relationships between variables in the form of a graph. The sparsity and clust…
Efficient algorithms for multivariate shape-constrained convex regression problems
Meixia Lin, Defeng Sun, Kim-Chuan Toh
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity…
Mesh Independence of a Majorized ABCD Method for Sparse PDE-constrained Optimization Problems
Xiaoliang Song, Defeng Sun, Kim-Chuan Toh
A majorized accelerated block coordinate descent (mABCD) method in Hilbert space is analyzed to solve a sparse PDE-constrained optimization problem via its dual. The finite element…
A Proximal Point Dual Newton Algorithm for Solving Group Graphical Lasso Problems
Yangjing Zhang, Ning Zhang, Defeng Sun +1
Undirected graphical models have been especially popular for learning the conditional independence structure among a large number of variables where the observations are drawn inde…
A sparse semismooth Newton based proximal majorization-minimization algorithm for nonconvex square-root-loss regression problems
Peipei Tang, Chengjing Wang, Defeng Sun +1
In this paper, we consider high-dimensional nonconvex square-root-loss regression problems and introduce a proximal majorization-minimization (PMM) algorithm for these problems. Ou…