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Modern numerical nonlinear optimization

Record Type:	Electronic resources : Monograph/item
Title/Author:	Modern numerical nonlinear optimizationby Neculai Andrei.
Author:	Andrei, Neculai.
Published:	Cham :Springer International Publishing :2022.
Description:	xxxiii, 807 p. :ill. (chiefly color), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Mathematical optimization.
Online resource:	https://doi.org/10.1007/978-3-031-08720-2
ISBN:	9783031087202$q(electronic bk.)

Modern numerical nonlinear optimization
Andrei, Neculai.

Modern numerical nonlinear optimization[electronic resource] /by Neculai Andrei. - Cham :Springer International Publishing :2022. - xxxiii, 807 p. :ill. (chiefly color), digital ;24 cm. - Springer optimization and its applications,v. 1951931-6836 ;. - Springer optimization and its applications ;v. 3..

1. Introduction -- 2. Fundamentals on unconstrained optimization -- 3. Steepest descent method -- 4. Newton method -- 5. Conjugate gradient methods -- 6. Quasi-Newton methods -- 7. Inexact Newton method -- 8. Trust-region method -- 9. Direct methods for unconstrained optimization -- 10. Constrained nonlinear optimization methods -- 11. Optimality conditions for nonlinear optimization -- 12. Simple bound optimization -- 13. Quadratic programming -- 14. Penalty and augmented Lagrangian -- 15. Sequential quadratic programming -- 16. Generalized reduced gradient with sequential linearization. (CONOPT) - 17. Interior-point methods -- 18. Filter methods -- 19. Interior-point filter line search (IPOPT) -- Direct methods for constrained optimization -- 20. Direct methods for constrained optimization -- Appendix A. Mathematical review -- Appendix B. SMUNO collection. Small scale optimization applications -- Appendix C. LACOP collection. Large-scale continuous nonlinear optimization applications -- Appendix D. MINPACK-2 collection. Large-scale unconstrained optimization applications -- References -- Author Index -- Subject Index.

This book includes a thorough theoretical and computational analysis of unconstrained and constrained optimization algorithms and combines and integrates the most recent techniques and advanced computational linear algebra methods. Nonlinear optimization methods and techniques have reached their maturity and an abundance of optimization algorithms are available for which both the convergence properties and the numerical performances are known. This clear, friendly, and rigorous exposition discusses the theory behind the nonlinear optimization algorithms for understanding their properties and their convergence, enabling the reader to prove the convergence of his/her own algorithms. It covers cases and computational performances of the most known modern nonlinear optimization algorithms that solve collections of unconstrained and constrained optimization test problems with different structures, complexities, as well as those with large-scale real applications. The book is addressed to all those interested in developing and using new advanced techniques for solving large-scale unconstrained or constrained complex optimization problems. Mathematical programming researchers, theoreticians and practitioners in operations research, practitioners in engineering and industry researchers, as well as graduate students in mathematics, Ph.D. and master in mathematical programming will find plenty of recent information and practical approaches for solving real large-scale optimization problems and applications.

ISBN: 9783031087202$q(electronic bk.)

Standard No.: 10.1007/978-3-031-08720-2doiSubjects--Topical Terms:

183292
Mathematical optimization.

LC Class. No.: QA402.5 / .A53 2022

Dewey Class. No.: 519.6

Modern numerical nonlinear optimization
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505 0 $a 1. Introduction -- 2. Fundamentals on unconstrained optimization -- 3. Steepest descent method -- 4. Newton method -- 5. Conjugate gradient methods -- 6. Quasi-Newton methods -- 7. Inexact Newton method -- 8. Trust-region method -- 9. Direct methods for unconstrained optimization -- 10. Constrained nonlinear optimization methods -- 11. Optimality conditions for nonlinear optimization -- 12. Simple bound optimization -- 13. Quadratic programming -- 14. Penalty and augmented Lagrangian -- 15. Sequential quadratic programming -- 16. Generalized reduced gradient with sequential linearization. (CONOPT) - 17. Interior-point methods -- 18. Filter methods -- 19. Interior-point filter line search (IPOPT) -- Direct methods for constrained optimization -- 20. Direct methods for constrained optimization -- Appendix A. Mathematical review -- Appendix B. SMUNO collection. Small scale optimization applications -- Appendix C. LACOP collection. Large-scale continuous nonlinear optimization applications -- Appendix D. MINPACK-2 collection. Large-scale unconstrained optimization applications -- References -- Author Index -- Subject Index.
520 $a This book includes a thorough theoretical and computational analysis of unconstrained and constrained optimization algorithms and combines and integrates the most recent techniques and advanced computational linear algebra methods. Nonlinear optimization methods and techniques have reached their maturity and an abundance of optimization algorithms are available for which both the convergence properties and the numerical performances are known. This clear, friendly, and rigorous exposition discusses the theory behind the nonlinear optimization algorithms for understanding their properties and their convergence, enabling the reader to prove the convergence of his/her own algorithms. It covers cases and computational performances of the most known modern nonlinear optimization algorithms that solve collections of unconstrained and constrained optimization test problems with different structures, complexities, as well as those with large-scale real applications. The book is addressed to all those interested in developing and using new advanced techniques for solving large-scale unconstrained or constrained complex optimization problems. Mathematical programming researchers, theoreticians and practitioners in operations research, practitioners in engineering and industry researchers, as well as graduate students in mathematics, Ph.D. and master in mathematical programming will find plenty of recent information and practical approaches for solving real large-scale optimization problems and applications.
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