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/

Zendy Plus

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

Zendy Tools

Zendy Open

We consider the problem of minimizing a polynomial function over the integerlattice. Though impossible in general, we use a known sufficient condition forthe existence of continuous minimizers to guarantee the existence of integerminimizers as well. In case this condition holds, we use sos programming tocompute the radius of a p-norm ball which contains all integer minimizers. Weprove that this radius is smaller than the radius known from the literature.Furthermore, we derive a new class of underestimators of the polynomialfunction. Using a Stellensatz from real algebraic geometry and again sosprogramming, we optimize over this class to get a strong lower bound on theinteger minimum. Our radius and lower bounds are evaluated experimentally. Theyshow a good performance, in particular within a branch and bound framework.

Norm Bounds and Underestimators for Unconstrained Polynomial Integer Minimization