CSC 2411 - Linear Programming and Combinatorial Optimization ∗ Lecture 7 : Ellipsoid Algorithm and Interior Point

This lecture provides an in-depth explanation of ellipsoid algorithm which was developed in 1979 by a Soviet mathematician L.G. Khachian. Ellipsoid algorithm is the first polynomial-time linear programming algorithm which also knows as Khachiyan’s algorithm to acknowledge Khachiyan’s discovery. This algorithm is fundamentally different from Simplex Algorithm in a sense that it does not exploit the combinatorial structure of linear programming and its based on binary search to determine whether a polyhedron is empty or not. We also present a high level description of interior point methods, which is the most commonly used algorithm for solving linear programming problems.