Undergraduate Convexity: From Fourier And Motzkin To Kuhn And Tucker

Book Details:

• Book Title: Undergraduate Convexity

• Author: Niels Lauritzen

• Publisher: World Scientific Publishing Company

• Language: English

• Edition: Illustrated Edition

• ISBN: 9789814452762

• Pages: 300

• Cover: Paperback

• Dimensions: 8.9 x 5.9 x 0.6 inches

About the Book:

Undergraduate Convexity by Niels Lauritzen is an accessible introduction to the theory of convex sets and convex functions, specifically designed for students in computer science, economics, and mathematics. Drawing from undergraduate teaching at Aarhus University, Lauritzen presents this subject in a clear, understandable way, emphasizing concrete computations and real-world examples to help students grasp the essential concepts.

The book begins with foundational topics such as linear inequalities and Fourier-Motzkin elimination. From there, it introduces more advanced concepts, including polyhedra, the double description method, and the simplex algorithm. As the theory develops, the book explores closed convex subsets, convex functions of one and several variables, and culminates with a discussion of convex optimization, covering key topics like the Karush-Kuhn-Tucker conditions, duality, and the interior point algorithm.

With its focus on practical applications and problem-solving, Undergraduate Convexity provides a thorough yet approachable guide to convexity, making it a valuable resource for students who want to understand the fundamental principles of this important area of mathematics and its relevance to optimization, economics, and computer science.