
Advancing Parametric Optimization
On Multiparametric Linear Complementarity Problems with Parameters in General Locations
Nathan Adelgren(Author)
Springer (Publisher)
Published on 22. January 2021
Book
Paperback/Softback
XII, 113 pages
978-3-030-61820-9 (ISBN)
Description
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
More details
Product info
Book
Series
Edition
1st ed. 2021
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
1 s/w Abbildung, 7 farbige Abbildungen, 7 farbige Tabellen
7 Tables, color; 7 Illustrations, color; 1 Illustrations, black and white; XII, 113 p. 8 illus., 7 illus. in color.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 8 mm
Weight
207 gr
ISBN-13
978-3-030-61820-9 (9783030618209)
DOI
10.1007/978-3-030-61821-6
Schweitzer Classification
Other editions
Additional editions

Nathan Adelgren
Advancing Parametric Optimization
On Multiparametric Linear Complementarity Problems with Parameters in General Locations
E-Book
01/2021
Springer
€69.54
Available for download
Person
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.
Content
1. Introduction.- 2. Background on mpLCP.- 3. Algebraic Properties of Invariancy Regions.- 4. Phase 2: Partitioning the Parameter Space.- 5. Phase 1: Determining an Initial Feasible Solution.- 6. Further Considerations.- 7. Assessment of Performance.- 8. Conclusion.- Appendix A. Tableaux for Example 2.1.- Appendix B. Tableaux for Example 2.2.- References.