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Advancing parametric optimization = ...

Adelgren, Nathan.

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Advancing parametric optimization = on multiparametric linear complementarity problems with parameters in general locations /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Advancing parametric optimization/ by Nathan Adelgren.
Reminder of title:	on multiparametric linear complementarity problems with parameters in general locations /
Author:	Adelgren, Nathan.
Published:	Cham :Springer International Publishing : : 2021.,
Description:	xii, 113 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Mathematical optimization. -
Online resource:	https://doi.org/10.1007/978-3-030-61821-6
ISBN:	9783030618216

Advancing parametric optimization = on multiparametric linear complementarity problems with parameters in general locations /
Adelgren, Nathan.

Advancing parametric optimizationon multiparametric linear complementarity problems with parameters in general locations /[electronic resource] :by Nathan Adelgren. - Cham :Springer International Publishing :2021. - xii, 113 p. :ill., digital ;24 cm. - SpringerBriefs in optimization,2190-8354. - SpringerBriefs in optimization..

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.

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.

ISBN: 9783030618216

Standard No.: 10.1007/978-3-030-61821-6doiSubjects--Topical Terms:

517763
Mathematical optimization.

LC Class. No.: QA402.5 / .A345 2021

Dewey Class. No.: 519.6

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505 0 $a 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.
520 $a 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.
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