Advancing Parametric Optimization

On Multiparametric Linear Complementarity Problems with Parameters in General Locations

Nathan Adelgren (Autor)

Buch | Softcover

XII, 113 Seiten

2021 | 1st ed. 2021
Springer International Publishing (Verlag)
978-3-030-61820-9 (ISBN)

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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

lt;b>_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.

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.

Erscheinungsdatum	25.01.2021
Reihe/Serie	SpringerBriefs in Optimization
Zusatzinfo	XII, 113 p. 8 illus., 7 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	209 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	multiobjective quadratic programming • multiparametric linear programming • Multiparametric Programming • multiparametric quadratic programming • polynomial optimization • Semi-algebraic sets
ISBN-10	3-030-61820-X / 303061820X
ISBN-13	978-3-030-61820-9 / 9783030618209
Zustand	Neuware