The Ellipsoid Method Generates Dual Variables

The Ellipsoid Method Generates Dual Variables

Ellipsoid Method

In this article we give an overview of the Ellipsoid Method. We start with a historic introduction and provide a basic algorithm in Section 2. Techniques to avoid two important assumptions required by this algorithm are considered in Section 2.2. After the discussion of some implementation aspects, we are able to show the polynomial running time of the Ellipsoid Method. The second section is cl...

The Ellipsoid Method: A Survey

In February 1979 a note by L. G. Khachiyan indicated how an ellipsoid method for linear programming can be implemented in polynomial time. This result has caused great excitement and stimulated a flood of technical papers. Ordinarily there would be no need for a survey of work so recent, but the current circumstances are obviously exceptional. Word of Khachiyan's result has spread extraordinari...

A modification of the ellipsoid method

We consider convex quadratic programming problem with convex quadratic constraints and suggest a modification of the well-known ellipsoid method based on using an ellipsoidal layer in the problem of circumscribing the minimum volume ellipsoid around of a part of a given ellipsoid. Our paper contains further development and improvement of the technique previously developed in [E.G88]. We show ho...

Ellipsoid Method for Linear Programming made simple

In this paper, ellipsoid method for linear programming is derived using only minimal knowledge of algebra and matrices. Unfortunately, most authors first describe the algorithm, then later prove its correctness, which requires a good knowledge of linear algebra.