Code producing the numerical results from the paper "Any-dimensional polynomial optimization via De Finetti theorems" by Eitan Levin and Venkat Chandrasekaran.
This repo contains the following scripts, which generate the results from the paper:
- Upper and lower bounds on the mean-field game from Example 6.1: mean_field_game_example.
- Lower bounds on symmetric functions from Example 6.4: symmetric_func_example.
This script requires the Matlab package Transition Matrices between Symmetric Polynomials to be available in Matlab's path.
Note in particular the function trans_matrix_p2q, which generates a matrix converting coefficients for the symmetric function to be minimized into coefficients for the freely-symmetrized lower bound on it in any one of six standard bases for symmteric polynomials. - Lower bounds on Ramsey multiplicity from Example 6.7: exhaustive_search_Ramsey.
This script requires the list of all graphs of sizes 4-10 in graph6 format, which can be downloaded from this website. - Upper and lower bounds on the injective homomorphism numbers from Example 6.10: graph_numbers.
All of the above scripts use YALMIP with MOSEK (which you could replace with an SDP solver of your choice).
In case of issues or questions, please email Eitan (eitanl@caltech.edu)