Description:

Title: Optimization of the Sherrington-Kirkpatrick Hamiltonian via Potential Hessian Ascent. 

Abstract: Recently, there has been significant progress on the question of optimizing mean-field spin glasses on the sphere and the hypercube. We quickly review this progress, and present our recent result on optimizing the Sherrington-Kirkpatrick Hamiltonian via a Hessian ascent algorithm. This resolves a question raised by Subag in his seminal work on optimizing full-RSB spin-glasses on the sphere. Time permitting, we will conclude with a brief discussion about the relationship between sum-of-squares semidefinite programs and spin-glass models on the sphere. Joint work(s) with David Jekel and Jonathan Shi.