This article shows how to solve linear programs of the form min Ax= b, x≥ 0 c⊤ x with n
variables in time O*((n ω+ n 2.5− α/2+ n 2+ 1/6) log (n/δ)), where ω is the exponent of matrix …

The penetration of distributed renewable energy sources in the distribution grid is increasing
considerably in the last years. This is one of the main causes that contributed to the growth …

Linear Programming: Foundations and Extensions Page 1 useful details of specific
implementations. The problems discussed arise in telecommunications, computer vision (point …

This book aims at developing a thorough understanding of the most general theory for
interior-point methods, a class of algorithms for convex optimization problems. The study of …

As the demand for energy continues to grow, optimization has risen to the forefront of power
engineering research and development. Continuing in the bestselling tradition of the first …

In this work, we first study in detail the formulation of the primal-dual interior-point method for
linear programming. We show that, contrary to popular belief, it cannot be viewed as a …

I was pleasantly surprised when I was asked by Springer-Verlag to prepare a second edition
of this volume on Linear Optimization and Extensions, which-not exactly contrary to my …

Interior methods for optimization were widely used in the 1960s, primarily in the form of
barrier methods. However, they were not seriously applied to linear programming because …

The main ideas of path following by predictor–corrector and piecewise-linear methods, and
their application in the direction of homotopy methods and nonlinear eigenvalue problems …

Optimization problems involving eigenvalues arise in many different mathematical
disciplines. This article is divided into two parts. Part I gives a historical account of the …