@MISC{Capozzo11anew, author = {Samantha Capozzo}, title = {A new proof of the ellipsoid algorithm}, year = {2011} }

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Abstract

Linear programming is described by Howard Karloff as “the process of minimizing a linear objective function, subject to a finite number of linear equality and inequality constraints”. Linear optimization is one of the main tools used in applied mathematics and economics. It finds applications in fields ranging from image processing to logistic distribution of goods. The first algorithm that was used to solve linear programs was the Simplex Method. Other popular algorithms are the Interior Point Methods. In 1979, Leonid Khachiyan invented the first ever polynomial-time algorithm to solve linear programs, the Ellipsoid Algorithm (see [13] for the first appearance). The algorithm is based on the geometry of ellipsoids and how a sequence of progressively smaller ellipsoids contains convex sets. Its ability to run in polynomial-time makes the Ellipsoid Algorithm an important theoretical tool that can be used as the basis of many other algorithmic applications in various fields. In my senior thesis, I will present the details of the Ellipsoid Algorithm and my work