Introduction to Linear Optimization. Book · January with 28, Reads. Publisher: Athena Scientific. Authors and Editors. Dimitris Bertsimas at. The book is a modern and unified introduction to linear optimization (linear programming, network flows and integer programming) at the PhD level. It covers , in. INTRODUCTION TO LINEAR OPTIMIZATION. Dimitris Bertsimas and John N. Tsitsiklis. Errata sheet. Last updated on 5/15/ The errata depend on the printing.
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The purpose of this book is to provide a unified, insightful, and modern treatment of the theory of integer optimization with an eye towards the future.
We have selected those topics that we feel have influenced the current state of the art and most importantly we feel will affect the future of the field. We depart from earlier treatments of integer optimization by placing significant emphasis on bertsimqs formulations, duality, algebra and most importantly geometry.
The chapters of the book are logically organized in four parts:. Formulations and relaxations includes Chapters and discusses how to formulate integer optimization problems, how to enhance the formulations to improve the quality of relaxations, how to obtain ideal formulations, the duality of integer optimizatioon and how to solve the resulting relaxations both practically and theoretically.
Algebra and geometry of integer optimization includes Chapters and develops the theory of lattices, oulines ideas from algebraic geometry that have had an impact on integer optimization, and most importantly discusses the geometry of integer optimization, a key feature berttsimas the book.
These chapters provide the building blocks for developing algorithms. Algorithms for integer optimization includes Chapters and develops cutting plane methods, integral basis methods, enumerative methods and approximation algorithms.
Introduction to Linear Optimization : Dimitris Bertsimas :
The key characteristic of our treatment is that our development of the algorithms is naturally optikization on the algebraic and geometric developments of Part II. Extensions of integer optimization includes Chapters 12 and 13, and treats mixed integer optimization and robust discrete optimization.
Both areas are practically significant as real world problems have very optimizatio both continous and discrete variables and have elements of uncertainty that need to be addressed in a tractable manner.
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The book is a modern and unified introduction to linear optimization linear programming, network flows and integer inttoduction at the PhD level. It covers, in addition to the classical material, all the recent developments in the field in the last ten years including the development of interior points, large scale optimization models and algorithms and complexity of linear optimization. It emphasizes the underlying geometry, intuition and applications of large scale systems.
Professor Dimitris Bertsimas
This book represents a departure from existing textbooks. Rather than covering methodology, the book introduces decision support systems through real world applications, and uses spreadsheets to model and solve problems.
It uses management science techniques statistics, simulation, probabilistic modeling and optimizationbut only as tools to facilitate problem solving. The chapters of the book are logically organized in four parts: