5 papers
Nonnegative Polynomials and Moment Problems on Algebraic Curves
Lorenzo Baldi, Grigoriy Blekherman, Rainer Sinn
The cone of nonnegative polynomials is of fundamental importance in real algebraic geometry, but its facial structure is understood in very few cases. We initiate a systematic stud…
Moments, Sums of Squares, and Tropicalization
Grigoriy Blekherman, Felipe Rincón, Rainer Sinn +2
We use tropicalization to study the duals to cones of nonnegative polynomials and sums of squares on a semialgebraic set . The truncated cones of moments of measures supported o…
Spurious local minima in nonconvex sum-of-squares optimization
Grigoriy Blekherman, Rainer Sinn, Mauricio Velasco +1
We study spurious second-order stationary points and local minima in a nonconvex low-rank formulation of sum-of-squares optimization on a real variety . We reformulate the probl…
Pythagoras Numbers for Ternary Forms
Grigoriy Blekherman, Alex Dunbar, Rainer Sinn
We study the Pythagoras numbers of real ternary forms, defined for each degree as the minimal number such that every degree ternary form which is a sum of…
Adjoints and Canonical Forms of Polypols
Kathlén Kohn, Ragni Piene, Kristian Ranestad +5
Polypols are natural generalizations of polytopes, with boundaries given by nonlinear algebraic hypersurfaces. We describe polypols in the plane and in 3-space that admit a unique…