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math.OC2026
Copositive Matrices with Ordered Off-Diagonal Entries
Grigoriy Blekherman, Santanu S. Dey, Alex Dunbar +1
We study copositive matrices which admit a decomposition into a sum of a positive semidefinite matrix and a matrix with nonnegative entries. Our main result shows that if the off-d…
math.OC2024
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…
math.OC2024
Convex Ternary Quartics Are SOS-Convex
Amir Ali Ahmadi, Grigoriy Blekherman, Pablo A. Parrilo
We prove that convex ternary quartic forms are sum-of-squares-convex (sos-convex). This result is in a meaningful sense the ``convex analogue'' a celebrated theorem of Hilbert from…