Interior Point Methods for Linear Optimization

Linear Optimization (LO) is one of the most widely applied and taught techniques in mathematics, with applications in many areas of science, commerce and industry. The dramatically increased interest in the subject is due mainly to advances in computer technology and the development of Interior Point Methods (IPMs) for LO.§This book provides a unified presentation of the field. The authors present a self-contained comprehensive interior point approach to both the theory of LO and algorithms for LO (design, convergence, complexity, asymptotic behaviour and computational issues). A common thread throughout the book is the role of strictly complementary solutions, which play a crucial role in the interior point approach and distinguishes the new approach from the classical Simplex-based approach.§The approach to LO in this book is new in many aspects. In particular the IPM and self-dual model based development of duality theory is surprisingly elegant. The algorithmic part of this book contains a complete discussion of many algorithmic variants, including predictor-corrector methods, partial updating, higher order methods and sensitivity and parametric analysis.§The comprehensive coverage of the subject, together with the clarity of presentation, ensures that this book will be an invaluable resource for researchers and professionals who wish to develop their understanding of LO and IPMs. Numerous exercises are provided to help consolidate understanding of the material and more than 45 figures are included to illustrate the characteristics of the algorithms. A general understanding of linear algebra and calculus is assumed. The first chapters provide a self-contained introduction to LO for readers who are unfamiliar with LO methods; however these chapters are also of interest for others who want to have a fresh look at the topic. §Audience§This book is intended for the optimization researcher community, advanced undergraduate and graduate students who are interested to learn the fundamentals and major variants of Interior Point Methods for linear optimization, who want to have a comprehensive introduction to Interior Point Methods that revolutionized the theory and practice of modern optimization.The era of interior point methods (IPMs) was initiated by N. Karmarkar s 1984 paper, which triggered turbulent research and reshaped almost all areas of optimization theory and computational practice. This book offers comprehensive coverage of IPMs. It details the main results of more than a decade of IPM research. Numerous exercises are provided to aid in understanding the material.