Search Results for author: Kim-Chuan Toh

Found 15 papers, 1 papers with code

Tractable hierarchies of convex relaxations for polynomial optimization on the nonnegative orthant

no code implementations13 Sep 2022 Ngoc Hoang Anh Mai, Victor Magron, Jean-Bernard Lasserre, Kim-Chuan Toh

We consider polynomial optimization problems (POP) on a semialgebraic set contained in the nonnegative orthant (every POP on a compact set can be put in this format by a simple translation of the origin).

Escaping Spurious Local Minima of Low-Rank Matrix Factorization Through Convex Lifting

no code implementations29 Apr 2022 Ching-pei Lee, Ling Liang, Tianyun Tang, Kim-Chuan Toh

This work proposes a rapid global solver for nonconvex low-rank matrix factorization (MF) problems that we name MF-Global.

An Inexact Projected Gradient Method with Rounding and Lifting by Nonlinear Programming for Solving Rank-One Semidefinite Relaxation of Polynomial Optimization

1 code implementation28 May 2021 Heng Yang, Ling Liang, Luca Carlone, Kim-Chuan Toh

In particular, we first design a globally convergent inexact projected gradient method (iPGM) for solving the SDP that serves as the backbone of our framework.

Learning Graph Laplacian with MCP

no code implementations22 Oct 2020 Yangjing Zhang, Kim-Chuan Toh, Defeng Sun

Motivated by the observation that the ability of the $\ell_1$ norm in promoting sparsity in graphical models with Laplacian constraints is much weakened, this paper proposes to learn graph Laplacian with a non-convex penalty: minimax concave penalty (MCP).

Estimation of sparse Gaussian graphical models with hidden clustering structure

no code implementations17 Apr 2020 Meixia Lin, Defeng Sun, Kim-Chuan Toh, Chengjing Wang

The sparsity and clustering structure of the concentration matrix is enforced to reduce model complexity and describe inherent regularities.

Efficient algorithms for multivariate shape-constrained convex regression problems

no code implementations26 Feb 2020 Meixia Lin, Defeng Sun, Kim-Chuan Toh

We prove that the least squares estimator is computable via solving a constrained convex quadratic programming (QP) problem with $(n+1)d$ variables and at least $n(n-1)$ linear inequality constraints, where $n$ is the number of data points.

A sparse semismooth Newton based proximal majorization-minimization algorithm for nonconvex square-root-loss regression problems

no code implementations27 Mar 2019 Peipei Tang, Chengjing Wang, Defeng Sun, Kim-Chuan Toh

In this paper, we consider high-dimensional nonconvex square-root-loss regression problems and introduce a proximal majorization-minimization (PMM) algorithm for these problems.

A dual Newton based preconditioned proximal point algorithm for exclusive lasso models

no code implementations1 Feb 2019 Meixia Lin, Defeng Sun, Kim-Chuan Toh, Yancheng Yuan

In addition, we derive the corresponding HS-Jacobian to the proximal mapping and analyze its structure --- which plays an essential role in the efficient computation of the PPA subproblem via applying a semismooth Newton method on its dual.

Convex Clustering: Model, Theoretical Guarantee and Efficient Algorithm

no code implementations4 Oct 2018 Defeng Sun, Kim-Chuan Toh, Yancheng Yuan

The perfect recovery properties of the convex clustering model with uniformly weighted all pairwise-differences regularization have been proved by Zhu et al. (2014) and Panahi et al. (2017).

A Fast Globally Linearly Convergent Algorithm for the Computation of Wasserstein Barycenters

no code implementations12 Sep 2018 Lei Yang, Jia Li, Defeng Sun, Kim-Chuan Toh

When the support points of the barycenter are pre-specified, this problem can be modeled as a linear programming (LP) problem whose size can be extremely large.

Efficient sparse semismooth Newton methods for the clustered lasso problem

no code implementations22 Aug 2018 Meixia Lin, Yong-Jin Liu, Defeng Sun, Kim-Chuan Toh

Based on the new formulation, we derive an efficient procedure for its computation.

An Efficient Semismooth Newton Based Algorithm for Convex Clustering

no code implementations ICML 2018 Yancheng Yuan, Defeng Sun, Kim-Chuan Toh

Clustering may be the most fundamental problem in unsupervised learning which is still active in machine learning research because its importance in many applications.

Max-Norm Optimization for Robust Matrix Recovery

no code implementations24 Sep 2016 Ethan X. Fang, Han Liu, Kim-Chuan Toh, Wen-Xin Zhou

This paper studies the matrix completion problem under arbitrary sampling schemes.

Matrix Completion

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