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Combinatorial, Linear, Integer and Nonlinear Optimization Apps

COLINA Grande

  • Textbook
  • © 2021

Overview

Authors:
  1. J. MacGregor Smith

    1. Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, USA

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  • Conceptually explains real world optimization problems which are then demonstrated with practical software apps
  • Brings optimization down to the students’ personal lives and experiences and gives them a marketable skill
  • Allows the students to implement a project idea from inception to implementation on their phone or tablet
  • Gives students access to state of the art software tools such as App Iniventor and AMPL optimization and mathematical programming software

Part of the book series: Springer Optimization and Its Applications (SOIA, volume 175)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xxi
    Download chapter PDF

  2. App Problem Formulation

    • J. MacGregor Smith
    Pages 1-17

  3. Combinatorial Optimization G(V, E)

    • J. MacGregor Smith
    Pages 19-82

  4. Linear Programming \(\sum c_jx_j, x_j \ \ge 0\ \forall j\)

    • J. MacGregor Smith
    Pages 83-132

  5. Integer Programming \(\sum c_j\delta _j, \delta _j \in \ \{0,1\} \ \ \forall j\)

    • J. MacGregor Smith
    Pages 133-178

  6. Nonlinear Programming \(\sum _i\sum _j c_{ij}x_ix_j, \ \forall \ (i,j)\)

    • J. MacGregor Smith
    Pages 179-230

  7. Back Matter

    Pages 231-259
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Keywords

About this book

This textbook provides an introduction to the use and understanding of optimization and modeling for upper-level undergraduate students in engineering and mathematics. The formulation of optimization problems is founded through concepts and techniques from operations research: Combinatorial Optimization, Linear Programming, and Integer and Nonlinear Programming (COLIN). Computer Science (CS) is also relevant and important given the applications of algorithms and Apps/algorithms (A) in solving optimization problems. Each chapter provides an overview of the main concepts of optimization according to COLINA, providing examples through App Inventor and AMPL software applications. All apps developed through the text are available for download. Additionally, the text includes links to the University of Wisconsin NEOS server, designed to handle more computing-intensive problems in complex optimization. Readers are encouraged to have some background in calculus, linear algebra, and relatedmathematics.

Reviews

“Throughout the book and the problems considered, the problem description is presented first, followed by a mathematical model, a solution algorithm and app, and a final evaluation. The layout of the book is easy to follow with many independent chunks that can be recorded during teaching if needed.” (Efstratios Rappos, zbMATH 1492.90082, 2022)

Authors and Affiliations

  • Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, USA

    J. MacGregor Smith

About the author

Professor Smith has a Ph.D. in Mechanical and Industrial Engineering (MIE) from the University of Illinois, Champaign-Urbana. He is currently a full professor in the MIE Department at the University of Massachusetts, Amherst. His research concerns performance modeling of stochastic and deterministic networks. His experience in teaching optimization laid the foundation for this COLINA Volume.

Bibliographic Information

  • Book Title: Combinatorial, Linear, Integer and Nonlinear Optimization Apps

  • Book Subtitle: COLINA Grande

  • Authors: J. MacGregor Smith

  • Series Title: Springer Optimization and Its Applications

  • DOI: https://doi.org/10.1007/978-3-030-75801-1

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2021

  • Hardcover ISBN: 978-3-030-75800-4Published: 18 October 2021

  • Softcover ISBN: 978-3-030-75803-5Published: 19 October 2022

  • eBook ISBN: 978-3-030-75801-1Published: 17 October 2021

  • Series ISSN: 1931-6828

  • Series E-ISSN: 1931-6836

  • Edition Number: 1

  • Number of Pages: XXI, 259

  • Number of Illustrations: 23 b/w illustrations, 191 illustrations in colour

  • Topics: Optimization, Operations Research, Management Science

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