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

The entropic barrier, studied by Bubeck and Eldan (Proc. Mach. Learn.Research, 2015), is a self-concordant barrier with asymptotically optimalself-concordance parameter. In this paper, we study the tropicalization of thecentral path associated with the entropic barrier, i.e., the logarithmic limitof this central path for a parametric family of linear programs defined overthe field of Puiseux series. Our main result is that the tropicalization of theentropic central path is a piecewise linear curve which coincides with thetropicalization of the logarithmic central path studied by Allamigeon et al.(SIAM J. Applied Alg. Geom., 2018). One consequence is that the number oflinear pieces in the tropical entropic central path can be exponential in thedimension and the number of inequalities defining the linear program.

The tropicalization of the entropic barrier