A Mathematical Primer on Linear Optimization

Diogo Gomes (u. a.)

ISBN 10: 1848903154 / ISBN 13: 9781848903159

Published by College Publications, 2019

About this Item

A Mathematical Primer on Linear Optimization | Diogo Gomes (u. a.) | Taschenbuch | Kartoniert / Broschiert | Englisch | 2019 | College Publications | EAN 9781848903159 | Verantwortliche Person für die EU: Libri GmbH, Europaallee 1, 36244 Bad Hersfeld, gpsr[at]libri[dot]de | Anbieter: preigu Print on Demand.

Seller Inventory # 117480169

Bibliographic Details

• Title: A Mathematical Primer on Linear Optimization
• Publisher: College Publications
• Publication Date: 2019
• Language: English
• ISBN 10: 1848903154
• ISBN 13: 9781848903159
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 234W x 156H x 15D millimeters 234 millimeters width by 156 millimeters height by 15 millimeters depth
• Weight: 409 grams
• Seller catalogs:
  • Bücher

About this title

Synopsis

The book provides a self-contained mathematical introduction to linear optimization for undergraduate students of Mathematics. This book is equally suitable for Science, Engineering, and Economics students who are interested in gaining a deeper understanding of the mathematical aspects of the subject. The linear optimization problem is analyzed from different perspectives: topological, algebraic, geometrical, logical, and algorithmic. Nevertheless, no previous knowledge of these subjects is required. The essential details are always provided in a special section at the end of each chapter. The technical material is illustrated with multiple examples, problems with fully-worked solutions, and a range of proposed exercises.

In Chapter 1, several formulations of the linear optimization problem are presented and related concerning admissible vectors and optimizers. Then, sufficient conditions for the existence of optimizers based on topological techniques are discussed in Chapter 2. The main objective of Chapter 3 is to provide a way for deciding whether or not an admissible vector is an optimizer, relying on Farkas' Lemma. In Chapter 4, linear algebra is used for computing optimizers via basic admissible vectors. A geometrical characterization of these vectors is the goal of Chapter 5. Duality is discussed in Chapter 6, giving yet a new technique for finding optimizers. An introduction to computational complexity is presented in Chapter 7 with the aim to analyze the efficiency of linear optimization algorithms. The complexity of a brute-force algorithm is shown not to be polynomial. Chapter 8 is targeted at the Simplex Algorithm. It includes the proof of its soundness and completeness and an explanation on its non-polynomial complexity. Finally, Chapter 9 concentrates on the integer optimization problem with an emphasis on totally unimodularity. An algorithm based on the Branch and Bound Technique is analyzed.