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

We study a primal-dual interior point method specialized to clusteredlow-rank semidefinite programs requiring high precision numerics, which arisefrom certain multivariate polynomial (matrix) programs through sums-of-squarescharacterizations and sampling. We consider the interplay of sampling andsymmetry reduction as well as a greedy method to obtain numerically good basesand sample points. We apply this to the computation of three-point bounds forthe kissing number problem, for which we show a significant speedup. Thisallows for the computation of improved kissing number bounds in dimensions $11$through $23$. The approach performs well for problems with bad numericalconditioning, which we show through new computations for the binary spherepacking problem.

Solving clustered low-rank semidefinite programs arising from polynomial optimization