Advancing Parametric Optimization
On Multiparametric Linear Complementarity Problems with Parameters in General Locations
Authors: Adelgren, Nathan
Free Preview- 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
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- About this book
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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
- About the authors
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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.
- Table of contents (8 chapters)
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Introduction
Pages 1-6
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Background on mpLCP
Pages 7-15
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Algebraic Properties of Invariancy Regions
Pages 17-30
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Phase 2: Partitioning the Parameter Space
Pages 31-65
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Phase 1: Determining an Initial Feasible Solution
Pages 67-78
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Table of contents (8 chapters)
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Bibliographic Information
- 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
- Copyright
- 2021
- Publisher
- Springer International Publishing
- Copyright Holder
- The Author(s), under exclusive license to Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-61821-6
- DOI
- 10.1007/978-3-030-61821-6
- Softcover ISBN
- 978-3-030-61820-9
- Series ISSN
- 2190-8354
- Edition Number
- 1
- Number of Pages
- XII, 113
- Number of Illustrations
- 1 b/w illustrations, 7 illustrations in colour
- Topics
