Turan Extremal Problem
The numerical optimal solution of our approximated model, matches the conjectured optimal function (left) and its Fourier transform (right) of the Turan's problem in 2D.
Numerical Evidence on the Turan Conjecture
Numerical Evidence on the Turan Conjecture
Turan’s extremal problem is an infinite-dimensional linear program, which has applications in number theory, where the variable is an L1 function and the constraints are on the Fourier transform of the variable over a convex body. With the FCO tool that we have developed, we aim to approximate the solution of the problem for various convex bodies to provide numerical evidence on the existing conjecture. Characterization of arbitrary convex sets in discrete domains, and evaluations of their volumes are among the challenges.