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Practical Mathematical Optimization

Basic Optimization Theory and Gradient-Based Algorithms

  • Jan A Snyman
  • Daniel N Wilke

Part of the Springer Optimization and Its Applications book series (SOIA, volume 133)

Table of contents

  1. Front Matter
    Pages i-xxvi
  2. Basic optimization theory

    1. Front Matter
      Pages 1-1
    2. Jan A. Snyman, Daniel N. Wilke
      Pages 3-40
    3. Jan A. Snyman, Daniel N. Wilke
      Pages 41-69
    4. Jan A. Snyman, Daniel N. Wilke
      Pages 71-112
    5. Jan A. Snyman, Daniel N. Wilke
      Pages 113-167
    6. Jan A. Snyman, Daniel N. Wilke
      Pages 169-193
  3. Gradient-based algorithms

    1. Front Matter
      Pages 195-195
    2. Jan A. Snyman, Daniel N. Wilke
      Pages 197-250
    3. Jan A. Snyman, Daniel N. Wilke
      Pages 251-271
    4. Jan A. Snyman, Daniel N. Wilke
      Pages 273-310
    5. Jan A. Snyman, Daniel N. Wilke
      Pages 311-340
  4. Back Matter
    Pages 341-372

About this book

Introduction

This textbook presents a wide range of tools for a course in mathematical optimization for upper undergraduate and graduate students in mathematics, engineering, computer science, and other applied sciences.  Basic optimization principles are presented with emphasis on gradient-based numerical optimization strategies and algorithms for solving both smooth and noisy discontinuous optimization problems. Attention is also paid to the difficulties of expense of function evaluations and the existence of multiple minima that often unnecessarily inhibit the use of gradient-based methods. This second edition addresses further advancements of gradient-only optimization strategies to handle discontinuities in objective functions. New chapters discuss the construction of surrogate models as well as new gradient-only solution strategies and numerical optimization using Python. A special Python module is electronically available (via springerlink) that makes the new algorithms featured in the text easily accessible and directly applicable. Numerical examples and exercises are included to encourage senior- to graduate-level students to plan, execute, and reflect on numerical investigations. By gaining a deep understanding of the conceptual material presented, students, scientists, and engineers will be  able to develop systematic and scientific numerical investigative skills.

 

Keywords

Mathematica algorithms linear optimization optimization programming Python multi-modal optimization non-smooth optimization discontinuous optimization Numerical Linear Algebra Hessian matrix approximations Gradient-only solution strategies Karush-Kuhn-Tucker theory Quadratic programming line search descent algorithm for unconstrained minimization Unconstrained one-dimensional minimization

Authors and affiliations

  • Jan A Snyman
    • 1
  • Daniel N Wilke
    • 2
  1. 1.Department of Mechanical and Aeronautical EngineeringUniversity of PretoriaPretoriaSouth Africa
  2. 2.Department of Mechanical and Aeronautical EngineeringUniversity of PretoriaPretoriaSouth Africa

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-77586-9
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-77585-2
  • Online ISBN 978-3-319-77586-9
  • Series Print ISSN 1931-6828
  • Series Online ISSN 1931-6836
  • Buy this book on publisher's site
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