Convexity and Optimization in Rn 1st Edition by Leonard D. Berkovitz (PDF)

Description

A comprehensive introduction to convexity and optimization inRn This book presents the mathematics of finite dimensionalconstrained optimization problems. It provides a basis for thefurther mathematical study of convexity, of more generaloptimization problems, and of numerical algorithms for the solutionof finite dimensional optimization problems. For readers who do nothave the requisite background in real analysis, the author providesa chapter covering this material. The text features abundantexercises and problems designed to lead the reader to a fundamentalunderstanding of the material. Convexity and Optimization in Rn provides detailed discussionof: * Requisite topics in real analysis * Convex sets * Convex functions * Optimization problems * Convex programming and duality * The simplex method A detailed bibliography is included for further study and an indexoffers quick reference. Suitable as a text for both graduate andundergraduate students in mathematics and engineering, thisaccessible text is written from extensively class-tested notes.

User’s Reviews

Editorial Reviews: Review “…a nice introduction to finite-dimensional optimization…”(Zentralblatt Math, Vol.991, No.16, 2002) “A textbook for a one-semester…course for students ofengineering, economics, operations research, and mathematics.”(SciTech Book News, Vol. 26, No. 2, June 2002) “…a fine introductory textbook that provides a solid introductionto the subject as well as a good foundation for further study…”(Mathematical Reviews, 2003a) From the Inside Flap A comprehensive introduction to convexity and optimization in Rn This book presents the mathematics of finite dimensional constrained optimization problems. It provides a basis for the further mathematical study of convexity, of more general optimization problems, and of numerical algorithms for the solution of finite dimensional optimization problems. For readers who do not have the requisite background in real analysis, the author provides a chapter covering this material. The text features abundant exercises and problems designed to lead the reader to a fundamental understanding of the material.Convexity and Optimization in Rn provides detailed discussion of:Requisite topics in real analysisConvex setsConvex functionsOptimization problemsConvex programming and dualityThe simplex methodA detailed bibliography is included for further study and an index offers quick reference. Suitable as a text for both graduate and undergraduate students in mathematics and engineering, this accessible text is written from extensively class-tested notes. From the Back Cover A comprehensive introduction to convexity and optimization in Rn This book presents the mathematics of finite dimensional constrained optimization problems. It provides a basis for the further mathematical study of convexity, of more general optimization problems, and of numerical algorithms for the solution of finite dimensional optimization problems. For readers who do not have the requisite background in real analysis, the author provides a chapter covering this material. The text features abundant exercises and problems designed to lead the reader to a fundamental understanding of the material.Convexity and Optimization in Rn provides detailed discussion of:Requisite topics in real analysisConvex setsConvex functionsOptimization problemsConvex programming and dualityThe simplex methodA detailed bibliography is included for further study and an index offers quick reference. Suitable as a text for both graduate and undergraduate students in mathematics and engineering, this accessible text is written from extensively class-tested notes. About the Author LEONARD D. BERKOVITZ, PhD, is Professor of Mathematics at Purdue University. He previously worked at the RAND Corporation and has served on the editorial boards of several journals, including terms as Managing Editor of the SIAM Journal on Control and as a member of the Editorial Committee of Mathematical Reviews. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book fully explains the convexity of math. The author really seems to know what he is talking about. It’s almost as if math is somehow fun again. Convexity and Optimization in Rn is just amazing. I cannot stand math, but after I read this book I have had an ephiphany. I used to get B’s in math. (actually I still do) But the point is, this book really helped me understand my mathmatics.The author is knowledgeable. I got to meet him at a book signing and he was incredibly nice, funny, and amazing. His words changed my life forever. This book is a MUST READ! TWO THUMBS UP!

⭐The contents of the book is well written, making for an easy yet mathematically rigorous introduction to linear optimization. For a third year mathematics undergraduate student, the material is very accessible and the first chapter can be covered in a few hours. The rigorous presentation, with proofs, of the mathematics might be challenging for students in economics and finance who don’t have the benefit of introductory courses in Analysis.This it not a book with optimization recipes or advanced algorithms in optimization. It only covers Georg Dantzigs’ Simplex method and Lagrangian Duality. Efficient interior Point methods, introduced in 1984 by Karmarkar.Still, as an introductory book to linear programming, the book deserves five stars.The Kindle edition is not recommended for the following reasons:1. Parts of the mathematical notation are missing making it virtually impossible to follow the fine points. Example: Proof of Lemma 3.4 (see attached screenshots, the second one is correct). There are many other “overlines” missing in the Kindle edition.2. A lesser nuisance: The links in the table of contents point to a few pages before the actual chapter.3. No page numbers.This book is around 100$. For this price I expect perfection in a digital edition. When the editors push a corrected update, I shall revise the review.

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