Markus Schweighofer

Global Optimization of Polynomials Using Gradient Tentacles and Sums of Squares

We consider the problem of computing the global infimum of a real polynomial

On the complexity of Schmüdgen's positivstellensatz

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Sums of Hermitian Squares and the BMV Conjecture

on

An algorithmic approach to Schmüdgen's Positivstellensatz

\mathbb R^n

Pure states, positive matrix polynomials and sums of hermitian squares

. Every global minimizer of

Exposed Faces of Semidefinitely Representable Sets

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Certificates for nonnegativity of polynomials with zeros on compact semialgebraic sets

lies on its gradient variety, i.e., the algebraic subset of

Pure states, nonnegative polynomials and sums of squares

\mathbb R^n

Algorithms for Weighted Sums of Squares Decomposition of Non-negative Univariate Polynomials

where the gradient of

Describing convex semialgebraic sets by linear matrix inequalities

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