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Ji'an Li

Publications and source records attributed to Ji'an Li.

2 recordsLinked to original sources
arXiv2026

Newton Method for Fixed-Support Doubly Entropic Wasserstein Barycenter

We study the fixed-support doubly regularized Wasserstein barycenter problem. Using the semi-dual formulation of entropic optimal transport, we reformulate the problem as a smooth, unconstrained, convex optimization problem in the dual variables. We then derive explicit expressions for the gradient and Hessian and develop an exact Newton method for high-accuracy barycenter computation. To improve scalability, we propose a sparse Newton variant that sparsifies the transport probability matrices, thereby reducing the cost of Hessian-vector products. We establish theoretical results for the proposed methods, including Hessian approximation bounds and convergence results. Experiments on synthetic and real datasets show that the sparse Newton method converges faster than

math.OC↗
arXiv2026

Inexact Bregman Sparse Newton Method for Efficient Optimal Transport

Computing exact Optimal Transport (OT) distances for large-scale datasets is computationally prohibitive. While entropy-regularized alternatives offer speed, they sacrifice precision and frequently suffer from numerical instability in high-accuracy regimes. To address these limitations, we propose the Inexact Bregman Sparse Newton (IBSN) method, which efficiently solves the exact OT problems. Our approach utilizes a Bregman proximal point framework through a sequence of semi-dual subproblems. By solving these subproblems inexactly, we significantly reduce per-iteration complexity while maintaining a theoretical guarantee of convergence to the true optimal plan. To further accelerate the algorithm, we develop a sparse Newton-type solver for the subproblem and employ a Hessian sparsification strategy that drastically lowers memory and time costs without sacrificing accuracy. We provide rigorous theoretical guarantees for the global convergence of the algorithm. Extensive experiments demonstrate that IBSN consistently outperforms state-of-the-art methods in both computational speed and solution precision.

math.OC↗