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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.
References
Tokhomirov, V. M. ``The Evolution of Methods of Convex Optimization.'' Amer. Math. Monthly 103, 65-71, 1996.