Maximum entropy and feasibility methods for convex and nonconvex inverse problems

We discuss informally two approaches to solving convex and nonconvex feasibility problems – via entropy optimization and via algebraic iterative methods. We shall highlight the advantages and disadvantages of each and give various related applications and limiting examples. While some of the results are very classical, they are not as well-known to practitioners as they should be. A key role is played by the Fenchel conjugate.