Nonlinear Optimization / Andrzej Ruszczynski.

Format:

Book

Author/Creator:

Ruszczynski, Andrzej, Author.

Language:

English

Subjects (All):

Mathematical optimization.

Nonlinear theories.

Physical Description:

1 online resource (463 p.)

Place of Publication:

Princeton, NJ : Princeton University Press, [2011]

Language Note:

English

Summary:

Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern topics such as optimality conditions and numerical methods for problems involving nondifferentiable functions, semidefinite programming, metric regularity and stability theory of set-constrained systems, and sensitivity analysis of optimization problems. Based on a decade's worth of notes the author compiled in successfully teaching the subject, this book will help readers to understand the mathematical foundations of the modern theory and methods of nonlinear optimization and to analyze new problems, develop optimality theory for them, and choose or construct numerical solution methods. It is a must for anyone seriously interested in optimization.

Contents:

Frontmatter

Contents

Preface

Chapter One. Introduction

PART 1. Theory

Chapter Two. Elements of Convex Analysis

Chapter Three. Optimality Conditions

Chapter Four. Lagrangian Duality

PART 2. Methods

Chapter Five. Unconstrained Optimization of Differentiable Functions

Chapter Six. Constrained Optimization of Differentiable Functions

Chapter Seven. Nondifferentiable Optimization

Appendix A. Stability of Set-Constrained Systems

Further Reading

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references (pages [431]-444) and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 26. Nov 2019)

ISBN:

9781400841059

1400841054

OCLC:

749265032