POEMA learning week 2: Day 2

Today was a full day. Starting with a triple whammy of POEMA ESR talks we got off to a running start. I will try my best to recall the highlights (based on my own limited understanding and memory) of the day:

ESR2 Andrew : Attacking polynomial optimization problems via the critical values route. This means computing the Jacobian of the system and then solving a determental system using a very subject specific algorithm Sparse FGLM algorithm.

ESR4 Alejandro : A verbose intro into real zero (RZ) polynomials from theory down to numerics. I had hoped to see a clearer link between RZ polynomials and the Generalized Lax Conjecture but hey-ho.

ESR12 Arefeh : Leveraging both primal and dual formulations in solving SDP's. Also extensions to sparse large SDP's and preconditioners for low rank SDPs. Considering how much I rely on SDP solvers I am painfully unaware of all the intricacies of their operation. I am glad Arefeh is an expert I can refer to should the need arise.

Prof. Dr. Thorsten Theobald gave a thorough intro to relative entropy programming. The gist was that one considers signomials instead of polynomials,( a polynomial with the monomials swapped out for exponentials). Optimization becomes a question of non negativity and this question is addressed by the arithmetic mean geometric mean inequality in contradistinction to the SOS approach from polynomial optimization.

There is a lot to digest, hopefully tomorrows soft skills training will be a change of pace.