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 first show that a continuous function f is nonnegative on a closed set$K\subseteq R^n$ if and only if (countably many) moment matrices of some signedmeasure $d\nu =fd\mu$ with support equal to K, are all positive semidefinite(if $K$ is compact $\mu$ is an arbitrary finite Borel measure with supportequal to K. In particular, we obtain a convergent explicit hierarchy ofsemidefinite (outer) approximations with {\it no} lifting, of the cone ofnonnegative polynomials of degree at most $d$. Wen used in polynomialoptimization on certain simple closed sets $\K$ (like e.g., the whole space$\R^n$, the positive orthant, a box, a simplex, or the vertices of thehypercube), it provides a nonincreasing sequence of upper bounds whichconverges to the global minimum by solving a hierarchy of semidefinite programswith only one variable. This convergent sequence of upper bounds complementsthe convergent sequence of lower bounds obtained by solving a hierarchy ofsemidefinite relaxations.

A new look at nonnegativity on closed sets and polynomial optimization