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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This work concentrates on optimization on Riemannian manifolds. TheLimited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm is a commonlyused quasi-Newton method for numerical optimization in Euclidean spaces.Riemannian LBFGS (RLBFGS) is an extension of this method to Riemannianmanifolds. RLBFGS involves computationally expensive vector transports as wellas unfolding recursions using adjoint vector transports. In this article, wepropose two mappings in the tangent space using the inverse second root andCholesky decomposition. These mappings make both vector transport and adjointvector transport identity and therefore isometric. Identity vector transportmakes RLBFGS less computationally expensive and its isometry is also veryuseful in convergence analysis of RLBFGS. Moreover, under the proposedmappings, the Riemannian metric reduces to Euclidean inner product, which ismuch less computationally expensive. We focus on the Symmetric PositiveDefinite (SPD) manifolds which are beneficial in various fields such as datascience and statistics. This work opens a research opportunity for extension ofthe proposed mappings to other well-known manifolds.

Vector Transport Free Riemannian LBFGS for Optimization on Symmetric Positive Definite Matrix Manifolds