Heuristic solutions to polynomial moment problems with some convex entropic objectives (Q1815703)

The author estimates a nonnegative density \(x\) on \(\mathbb{R}^n\), given some of its algebraic or trigonometric moments. The maximum entropy method is to introduce an entropy-like objective function and then solve a convex optimal control problem. Special structures of the problem have been discovered when some particular entropies are used, which include the Boltzmann-Shannon entropy and Burg's entropy. Useful linear relationships among the moments lead to very fast and effective algorithms. Some numerical aspects of the problem are presented.