The problem of maximizing a linear function over a convex polyhedron, also known as Operations Research or Optimization Theory. The general problem of convex optimization is to find the minimum of a convex (or quasiconvex) function on a Finite-dimensional convex body . Methods of solution include Levin's algorithm and the method of circumscribed Ellipsoids, also called the Nemirovsky-Yudin-Shor method.
Tokhomirov, V. M. ``The Evolution of Methods of Convex Optimization.'' Amer. Math. Monthly 103, 65-71, 1996.