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Advancing Parametric Optimization

On Multiparametric Linear Complementarity Problems with Parameters in General Locations

  • Book
  • © 2021

Overview

Authors:
  1. Nathan Adelgren

    1. Department of Mathematics and Computer Science, Edinboro University, Edinboro, USA

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  • Theory merges many concepts from mathematical optimization and algebraic geometry
  • Answers many natural questions that might occur to the reader
  • Extensive bibliography provides additional topical resource

Part of the book series: SpringerBriefs in Optimization (BRIEFSOPTI)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction

    • Nathan Adelgren
    Pages 1-6

  3. Background on mpLCP

    • Nathan Adelgren
    Pages 7-15

  4. Algebraic Properties of Invariancy Regions

    • Nathan Adelgren
    Pages 17-30

  5. Phase 2: Partitioning the Parameter Space

    • Nathan Adelgren
    Pages 31-65

  6. Phase 1: Determining an Initial Feasible Solution

    • Nathan Adelgren
    Pages 67-78

  7. Further Considerations

    • Nathan Adelgren
    Pages 79-87

  8. Assessment of Performance

    • Nathan Adelgren
    Pages 89-93

  9. Conclusion

    • Nathan Adelgren
    Pages 95-95

  10. Back Matter

    Pages 97-113
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Keywords

About this book

The theory presented in this work merges many concepts from mathematical optimization and real algebraic geometry. When unknown or uncertain data in an optimization problem is replaced with parameters, one obtains a multi-parametric optimization problem whose optimal solution comes in the form of a function of the parameters.The theory and methodology presented in this work allows one to solve both Linear Programs and convex Quadratic Programs containing parameters in any location within the problem data as well as multi-objective optimization problems with any number of convex quadratic or linear objectives and linear constraints. Applications of these classes of problems are extremely widespread, ranging from business and economics to chemical and environmental engineering. Prior to this work, no solution procedure existed for these general classes of problems except for the recently proposed algorithms

Authors and Affiliations

  • Department of Mathematics and Computer Science, Edinboro University, Edinboro, USA

    Nathan Adelgren

About the author

​Nathan Adelgren earned his Ph.D. in Mathematical Sciences from Clemson University in 2016. He is currently an Associate Professor in the Department of Mathematics and Computer Science at Edinboro University in Edinboro, PA. His research interests are in the general field of Operations Research and include developing novel solution procedures for nontraditional optimization problems in the form of multicriteria, multiparametric, and mixed-integer programs as well as various combinations of these.

Bibliographic Information

  • Book Title: Advancing Parametric Optimization

  • Book Subtitle: On Multiparametric Linear Complementarity Problems with Parameters in General Locations

  • Authors: Nathan Adelgren

  • Series Title: SpringerBriefs in Optimization

  • DOI: https://doi.org/10.1007/978-3-030-61821-6

  • Publisher: Springer Cham

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

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

  • Softcover ISBN: 978-3-030-61820-9Published: 22 January 2021

  • eBook ISBN: 978-3-030-61821-6Published: 21 January 2021

  • Series ISSN: 2190-8354

  • Series E-ISSN: 2191-575X

  • Edition Number: 1

  • Number of Pages: XII, 113

  • Number of Illustrations: 1 b/w illustrations, 7 illustrations in colour

  • Topics: Optimization, Algebraic Geometry

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