This reprint of the 1969 book of the same name is a concise, rigorous, yet accessible, account of the fundamentals of constrained optimization theory. Many problems arising in diverse fields such as machine learning, medicine, chemical engineering, structural design, and airline scheduling can be reduced to a constrained optimization problem. This book provides readers with the fundamentals needed to study and solve such problems. Beginning with a chapter on linear inequalities and theorems of the alternative, basics of convex sets and separation theorems are then derived based on these theorems. This is followed by a chapter on convex functions that includes theorems of the alternative for such functions. These results are used in obtaining the saddlepoint optimality conditions of nonlinear programming without differentiability assumptions.
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Book Description
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Book Description
A concise, rigorous, yet accessible, account of the fundamentals of constrained optimization theory. Many problems arising in diverse fields such as machine learning, medicine, chemical engineering, structural design, and scheduling can be reduced to a constrained optimization problem. Provides readers with the fundamentals needed to study and solve such problems.
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3 of 5 people found the following review helpful:
5.0 out of 5 stars
Learn how to write a clear and didactic math book,
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This review is from: Nonlinear Programming (Classics in Applied Mathematics) (Paperback)
This book addresses only Nonlinear Programming Theory.You will not find any algorithms, so that this book is not very practical. The title should be "Nonlinear Programming Theory" Why 5 stars ? Main factor: The writing style. That is, what I like most in this book is the way that Mangasarian wrote it. References to all important equations, definitions, etc. No "verbose excessive use" of english to explain math subjects but well defined equations. Concise exposition and proof of theorems using math simbols. That is: Math simbols to explain mathematics. Very clear style. A very good example of how to write an excellent, didactic, precise and clear math book.
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Inside This Book
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First Sentence:
The nonlinear programming problem that will concern us has three fundamental ingredients: a finite number of real variables, a finite number of constraints which the variables must satisfy, and a function of the variables which must be minimized (or maximized). Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Fritz John, Problem Let, Corollary Let, Berge-Ghouila Houri New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The nonlinear programming problem that will concern us has three fundamental ingredients: a finite number of real variables, a finite number of constraints which the variables must satisfy, and a function of the variables which must be minimized (or maximized). Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Fritz John, Problem Let, Corollary Let, Berge-Ghouila Houri New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
100
books
cite this book:
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- Practical Optimization by Philip E. Gill on 9 pages
- Optimization, Volume 1 (Handbooks in Operations Research and Management Science) by George L. Nemhauser on 5 pages
- Mathematics of Optimization: Smooth and Nonsmooth Case by Giorgio Giorgi on page 196, page 357, and page 499
- Generalized Convexity, Generalized Monotonicity and Applications: Proceedings of the 7th International Symposium on Generalized Convexity and ... Optimization and Its Applications (closed)) by Andrew Eberhard on page 145, page 158, and page 337
- Inherently Parallel Algorithms in Feasibility and Optimization and their Applications (Studies in Computational Mathematics) by D. Butnariu on page 182, page 216, and page 305
See all 100 books citing this book
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