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adelgren nathan - advancing parametric optimization

Advancing Parametric Optimization On Multiparametric Linear Complementarity Problems with Parameters in General Locations




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Dettagli

Genere:Libro
Lingua: Inglese
Editore:

Springer

Pubblicazione: 01/2021
Edizione: 1st ed. 2021





Trama

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




Sommario

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.




Autore

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.










Altre Informazioni

ISBN:

9783030618209

Condizione: Nuovo
Collana: SpringerBriefs in Optimization
Dimensioni: 235 x 155 mm Ø 454 gr
Formato: Brossura
Illustration Notes:XII, 113 p. 8 illus., 7 illus. in color.
Pagine Arabe: 113
Pagine Romane: xii


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