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.
Convex Optimization Theory
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ReferencesTokhomirov, V. M. "The Evolution of Methods of Convex Optimization." Amer. Math. Monthly 103, 65-71, 1996.
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Weisstein, Eric W. "Convex Optimization Theory." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ConvexOptimizationTheory.html