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NewVEM: A Newton Vertex Exchange Method for a Class of Constrained Self-Concordant Minimization Problems
Ling Liang, Kim-Chuan Toh, Haizhao Yang
We propose \textbf{NewVEM}, a Newton vertex exchange method for efficiently solving self-concordant minimization problems under generalized simplex constraints. The algorithm featu…
Nesterov's Accelerated Jacobi-Type Methods for Large-scale Symmetric Positive Semidefinite Linear Systems
Ling Liang, Qiyuan Pang, Kim-Chuan Toh +1
Solving symmetric positive semidefinite linear systems is an essential task in many scientific computing problems. While Jacobi-type methods, including the classical Jacobi method…
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…
On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences
Hoang Anh Tran, Toh Kim-Chuan
The moment-SOS hierarchy is a widely applicable framework to address polynomial optimization problems over basic semi-algebraic sets based on positivity certificates of polynomial.…
Tractable hierarchies of convex relaxations for polynomial optimization on the nonnegative orthant
Ngoc Hoang Anh Mai, Victor Magron, Jean-Bernard Lasserre +1
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 tra…
An Inexact Halpern Iteration with Application to Distributionally Robust Optimization
Ling Liang, Zusen Xu, Kim-Chuan Toh +1
The Halpern iteration for solving monotone inclusion problems has gained increasing interests in recent years due to its simple form and appealing convergence properties. In this p…