Graduate Texts in Mathematics bridge the gap between passive study and creative
understanding, offering graduate-level introductions to advanced topics in mathematics. The …

A bstract We introduce SDPB: an open-source, parallelized, arbitrary-precision semidefinite
program solver, designed for the conformal bootstrap. SDPB significantly outperforms less …

We consider the problem of minimizing a polynomial over a semialgebraic set defined by
polynomial equations and inequalities, which is NP-hard in general. Hierarchies of …

Hilbert's 17th Problem asks whether a real positive semidefinite polynomial can be
expressed as a sum of squares of rational functions. Artin answered “yes” in the 1920's …

We investigate the representation of multivariate symmetric polynomials as sum of squares,
as well as the effective computation of this decomposition. Since this task is solved using …

Given that an element a in a ring A is a sum of squares in A, say (l F Xa;, it is natural to ask
for the smallest t (called the length of a in A) for which such an expression is possible. For …

Moment and polynomial optimization has received high attention in recent decades. It has
beautiful theory and efficient methods, as well as broad applications for various …

In 1888, Hilbert [6] studied the problem of whether a positive semi-definite (real) polynomial
must be a sum of squares of other (real) polynomials. Upon homogenization, it is sufficient to …

The release of SOSTOOLS v4. 00 comes as we approach the 20th anniversary of the
original release of SOSTOOLS v1. 00 back in April, 2002. SOSTOOLS was originally …

We completely characterize sections of the cones of nonnegative polynomials, convex
polynomials and sums of squares with polynomials supported on circuits, a genuine class of …