English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

The discrete optimal transport (OT) problem, which offers an effectivecomputational tool for comparing two discrete probability distributions, hasrecently attracted much attention and played essential roles in many modernapplications. This paper proposes to solve the discrete OT problem by applyinga squared smoothing Newton method via the Huber smoothing function for solvingthe corresponding KKT system directly. The proposed algorithm admits appealingconvergence properties and is able to take advantage of the solution sparsityto greatly reduce computational costs. Moreover, the algorithm can be extendedto solve problems with similar structures including the Wasserstein barycenter(WB) problem with fixed supports. To verify the practical performance of theproposed method, we conduct extensive numerical experiments to solve a largeset of discrete OT and WB benchmark problems. Our numerical results show thatthe proposed method is efficient compared to state-of-the-art linearprogramming (LP) solvers. Moreover, the proposed method consumes less memorythan existing LP solvers, which demonstrates the potential usage of ouralgorithm for solving large-scale OT and WB problems.

A Sparse Smoothing Newton Method for Solving Discrete Optimal Transport Problems