Optimization Models

This accessible textbook demonstrates how to recognize, simplify, model and solve optimization problems – and apply these principles to new projects.

Giuseppe C. Calafiore (Author), Laurent El Ghaoui (Author)

9781107050877, Cambridge University Press

Hardback, published 31 October 2014

650 pages, 352 b/w illus. 126 exercises
25.3 x 19.6 x 3.4 cm, 1.57 kg

'In Optimization Models, Calafiore and El Ghaoui have created a beautiful and very much needed on-ramp to the world of modern mathematical optimization and its wide range of applications. They lead an undergraduate, with not much more than basic calculus behind her, from the basics of linear algebra all the way to modern optimization-based machine learning, image processing, control, and finance, to name just a few applications. Until now, these methods and topics were accessible only to graduate students in a few fields, and the few undergraduates who brave the daunting prerequisites. The book's seamless integration of mathematics and applications, and its focus on modeling practical problems and algorithmic solution methods, will be very appealing to a wide audience.' Stephen Boyd, Stanford University, California

Emphasizing practical understanding over the technicalities of specific algorithms, this elegant textbook is an accessible introduction to the field of optimization, focusing on powerful and reliable convex optimization techniques. Students and practitioners will learn how to recognize, simplify, model and solve optimization problems - and apply these principles to their own projects. A clear and self-contained introduction to linear algebra demonstrates core mathematical concepts in a way that is easy to follow, and helps students to understand their practical relevance. Requiring only a basic understanding of geometry, calculus, probability and statistics, and striking a careful balance between accessibility and rigor, it enables students to quickly understand the material, without being overwhelmed by complex mathematics. Accompanied by numerous end-of-chapter problems, an online solutions manual for instructors, and relevant examples from diverse fields including engineering, data science, economics, finance, and management, this is the perfect introduction to optimization for undergraduate and graduate students.

1. Introduction
Part I. Linear Algebra: 2. Vectors
3. Matrices
4. Symmetric matrices
5. Singular value decomposition
6. Linear equations and least-squares
7. Matrix algorithms
Part II. Convex Optimization: 8. Convexity
9. Linear, quadratic and geometric models
10. Second-order cone and robust models
11. Semidefinite models
12. Introduction to algorithms
Part III. Applications: 13. Learning from data
14. Computational finance
15. Control problems
16. Engineering design.

Subject Areas: Communications engineering / telecommunications [TJK], Electronics engineering [TJF], Mechanical engineering [TGB], Engineering: general [TBC], Probability & statistics [PBT], Operational research [KJT], Economic statistics [KCHS]