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© 2019

Nonlinear Optimization

Benefits

  • Textbook for convex optimization and non-convex optimization courses

  • Contains exercises with select solutions

  • Features model building, real problems, and applications of optimization models

  • Provides numerical approaches to solve nonlinear optimization problems

Textbook

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Francisco J. Aragón, Miguel A. Goberna, Marco A. López, Margarita M. L. Rodríguez
    Pages 1-51
  3. Analytical Optimization

    1. Front Matter
      Pages 53-53
    2. Francisco J. Aragón, Miguel A. Goberna, Marco A. López, Margarita M. L. Rodríguez
      Pages 55-89
    3. Francisco J. Aragón, Miguel A. Goberna, Marco A. López, Margarita M. L. Rodríguez
      Pages 91-116
    4. Francisco J. Aragón, Miguel A. Goberna, Marco A. López, Margarita M. L. Rodríguez
      Pages 117-180
  4. Numerical Optimization

    1. Front Matter
      Pages 181-181
    2. Francisco J. Aragón, Miguel A. Goberna, Marco A. López, Margarita M. L. Rodríguez
      Pages 183-252
    3. Francisco J. Aragón, Miguel A. Goberna, Marco A. López, Margarita M. L. Rodríguez
      Pages 253-309
  5. Francisco J. Aragón, Miguel A. Goberna, Marco A. López, Margarita M. L. Rodríguez
    Pages C1-C1
  6. Back Matter
    Pages 311-350

About this book

Introduction

This textbook on nonlinear optimization focuses on model building, real world problems, and applications of optimization models to natural and social sciences. Organized into two parts, this book may be used as a primary text for courses on convex optimization and non-convex optimization. Definitions, proofs, and numerical methods are well illustrated and all chapters contain compelling exercises. The exercises emphasize fundamental theoretical results on optimality and duality theorems, numerical methods with or without constraints, and derivative-free optimization. Selected solutions are given. Applications to theoretical results and numerical methods are highlighted to help students comprehend methods and techniques.

Keywords

convexity coercivity linear regression Jensen's inequalities polynomial regression Lagrange duality Nelder and Mead method Fermat-Steiner problem Quasi-Newton methods optimization problems unconstrained optimization geometric optimizqtion quadratic optimiztion wolfe duality optimization algorithms line search methods gradient methods derivative-free optimization methods constrained optimization

Authors and affiliations

  1. 1.Department of MathematicsUniversity of AlicanteAlicanteSpain
  2. 2.Department of MathematicsUniversity of AlicanteAlicanteSpain
  3. 3.Department of MathematicsUniversity of AlicanteAlicanteSpain
  4. 4.Department of MathematicsUniversity of AlicanteAlicanteSpain

About the authors

Francisco J. Aragón (Ramón y Cajal Researcher), Miguel A. Goberna (Full Professor), Marco A. López (Full Professor), and Margarita M. L. Rodríguez (Associate Professor) are members of the Optimization Laboratory at the University of Alicante. Marco A. López is also Honorary Adjunct Professor of CIAO, Federation University, Ballarat (Australia). This group was created in the 1980s by the 2nd and 3rd authors, and works on the theory and methods for optimization problems. In particular, they have analyzed ordinary, semi-infinite, and infinite optimization problems from different perspectives (e.g., optimality, duality, stability, sensitivity and robustness), and have contributed with various numerical methods for linear and convex semi-infinite optimization problems and systems, together with new splitting algorithms for tackling feasibility and optimization problems.

Miguel A. Goberna and Marco A. López are co-authors of the books Linear Semi-Infinite Optimization (J. Wiley, 1998) and Post-Optimal Analysis in Linear Semi-Infinite Optimization (SpringerBrief, 2014).


Bibliographic information

  • Book Title Nonlinear Optimization
  • Authors Francisco J. Aragón
    Miguel A. Goberna
    Marco A. López
    Margarita M.L. Rodríguez
  • Series Title Springer Undergraduate Texts in Mathematics and Technology
  • Series Abbreviated Title Spr.Undergrad.Text.Math.,Technology
  • DOI https://doi.org/10.1007/978-3-030-11184-7
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-030-11183-0
  • eBook ISBN 978-3-030-11184-7
  • Series ISSN 1867-5506
  • Series E-ISSN 1867-5514
  • Edition Number 1
  • Number of Pages XIV, 350
  • Number of Illustrations 87 b/w illustrations, 106 illustrations in colour
  • Topics Optimization
  • Buy this book on publisher's site
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Reviews

“The book can be used for ‘upper-level undergraduate students of mathematics and statistics, and graduate students of industrial engineering.’ … I would recommend it to students for further reading and to colleagues for its nicely illustrated material that may be used for designing their lectures on nonlinear optimization.” (Martin Schmidt, SIAM Review, Vol. 62 (2), 2020)

“This book is a valuable contribution to optimization, its theory, methods and applications ... . Applications to theoretical results and numerical methods are highlighted to help readers, e.g., students, in order to understand and learn approaches and methods. This excellent book is clearly and well structured, analytically deep, well exemplified, beautifully illustrated, and written with care and taste.” (Gerhard-Wilhelm, WeberJoanna Majchrzak and Erik Kropat, zbMATH 1423.90001, 2019)