15 citations · 47 across the 26 of their papers we have counts for
4 papers · 1 filter
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…
Nonnegativity certificates on real algebraic surfaces
Grigoriy Blekherman, Rainer Sinn, Gregory G. Smith +1
We introduce tools for transferring nonnegativity certificates for global sections between line bundles on real algebraic surfaces. As applications, we improve Hilbert's degree bou…
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…