12 papers
Convex Relaxations for the Optimization of Markov Processes
Hongyi Zhang, Yuehaw Khoo, Tianyun Tang
In this paper, we study the problem of optimizing Markov processes that interpolate between two prescribed probability distributions while minimizing a given cost. The main computa…
Convex relaxation approaches for high-dimensional optimal transport
Yuehaw Khoo, Tianyun Tang
Optimal transport (OT) is a powerful tool in mathematics and data science but faces severe computational and statistical challenges in high dimensions. We propose convex relaxation…
A preconditioned augmented Lagrangian method for solving semidefinite programming problems
Tianyun Tang, Kim-Chuan Toh
In this work, we propose a preconditioned augmented Lagrangian method (ALM) for solving semidefinite programming (SDP) problems. The preconditioner is implemented via a weighted pe…
On the efficient computation of proximal operators of affine-constrained nonconvex functions
Di Hou, Tianyun Tang, Kim-Chuan Toh +1
Proximal operators with affine constraints arise in numerous models in nonconvex projection, composite optimization, and structured regularization. However, their efficient computa…
Accelerating nuclear-norm regularized low-rank matrix optimization through Burer-Monteiro decomposition
Ching-pei Lee, Ling Liang, Tianyun Tang +1
This work proposes a rapid algorithm, BM-Global, for nuclear-norm-regularized convex and low-rank matrix optimization problems. BM-Global efficiently decreases the objective value…
A Low-rank Augmented Lagrangian Method for Polyhedral-SDP and Moment-SOS Relaxations of Polynomial Optimization
Di Hou, Tianyun Tang, Kim-Chuan Toh
Polynomial optimization problems (POPs) can be reformulated as geometric convex conic programs, as shown by Kim, Kojima, and Toh (SIOPT 30:1251-1273, 2020), though such formulation…