- English
- ePUB (mobile friendly)
- Available on iOS & Android
About this book
Discover the practical impacts of current methods of optimization with this approachable, one-stop resource
Linear and Convex Optimization: A Mathematical Approach delivers a concise and unified treatment of optimization with a focus on developing insights in problem structure, modeling, and algorithms. Convex optimization problems are covered in detail because of their many applications and the fast algorithms that have been developed to solve them.
Experienced researcher and undergraduate teacher Mike Veatch presents the main algorithms used in linear, integer, and convex optimization in a mathematical style with an emphasis on what makes a class of problems practically solvable and developing insight into algorithms geometrically. Principles of algorithm design and the speed of algorithms are discussed in detail, requiring no background in algorithms.
The book offers a breadth of recent applications to demonstrate the many areas in which optimization is successfully and frequently used, while the process of formulating optimization problems is addressed throughout.
Linear and Convex Optimization contains a wide variety of features, including:
- Coverage of current methods in optimization in a style and level that remains appealing and accessible for mathematically trained undergraduates
- Enhanced insights into a few algorithms, instead of presenting many algorithms in cursory fashion
- An emphasis on the formulation of large, data-driven optimization problems
- Inclusion of linear, integer, and convex optimization, covering many practically solvable problems using algorithms that share many of the same concepts
- Presentation of a broad range of applications to fields like online marketing, disaster response, humanitarian development, public sector planning, health delivery, manufacturing, and supply chain management
Ideal for upper level undergraduate mathematics majors with an interest in practical applications of mathematics, this book will also appeal to business, economics, computer science, and operations research majors with at least two years of mathematics training. Software to accompany the text can be found here: https://www.gordon.edu/michaelveatch/optimization
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Information
Table of contents
- Cover
- Table of Contents
- Linear and Convex Optimization
- Copyright
- Preface
- About the Companion Website
- 1 Introduction to Optimization Modeling
- 2 Linear Programming Models
- 3 Linear Programming Formulations
- 4 Integer Programming Models
- 5 Iterative Search Algorithms
- 6 Convexity
- 7 Geometry and Algebra of LPs
- 8 Duality Theory
- 9 Simplex Method
- 10 Sensitivity Analysis
- 11 Algorithmic Applications of Duality
- 12 Integer Programming Theory
- 13 Integer Programming Algorithms
- 14 Convex Programming: Optimality Conditions
- 15 Convex Programming: Algorithms
- A Linear Algebra and Calculus Review
- Bibliography
- Index
- End User License Agreement