Michel X . Goemans 7 . Lecture notes on the ellipsoid algorithm

7. Lecture Notes on the Ellipsoid Algorithm

The simplex algorithm was the first algorithm proposed for linear programming, and although the algorithm is quite fast in practice, no variant of it is known to be polynomial time. The Ellipsoid algorithm is the first polynomial-time algorithm discovered for linear programming. The Ellipsoid algorithm was proposed by the Russian mathematician Shor in 1977 for general convex optimization proble...

Optional Lecture 3 : Interior Point Method

This file of notes serves as a reference for Zeyuan himself about the materials to be delivered in class. It copies a lot of materials from Prof Michel X. Goemans’ lecture notes on 6.854 in 1994, (see http: //www-math.mit.edu/~goemans/notes-lp.ps), and Prof Sven O. Krumke’s report on interior point methods (see http://optimierung.mathematik.uni-kl.de/~krumke/Notes/interior-lecture. pdf). Ye’s i...

Lecture notes on the ellipsoid algorithm

The simplex algorithm was the first algorithm proposed for linear programming, and although the algorithm is quite fast in practice, no variant of it is known to be polynomial time. The Ellipsoid algorithm is the first polynomial-time algorithm discovered for linear programming. The Ellipsoid algorithm was proposed by the Russian mathematician Shor in 1977 for general convex optimization proble...

8.438 Advanced Combinatorial Optimization 2 Iwata and Orlin's Algorithm

Given a finite set V with n elements, a function f : 2 → Z is submodular if for all X,Y ⊆ V , f(X ∪ Y ) + f(X ∩ Y ) ≤ f(X) + f(Y ). Submodular functions frequently arise in combinatorial optimization. For example, the cut function in a weighted undirected graph and the rank function of a matroid are both submodular. Submodular function minimization is the problem of finding the global minimum o...

Lecture 16: Approximation Algorithms