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＜電子ブック＞
Modern Numerical Nonlinear Optimization / by Neculai Andrei
(Springer Optimization and Its Applications. ISSN:19316836 ; 195)

版	1st ed. 2022.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2022
本文言語	英語
大きさ	XXXIII, 807 p. 117 illus., 108 illus. in color : online resource
著者標目	*Andrei, Neculai author SpringerLink (Online service)
件　名	LCSH:Mathematical optimization LCSH:Mathematics -- Data processing  全ての件名で検索 LCSH:Algorithms FREE:Optimization FREE:Computational Mathematics and Numerical Analysis FREE:Algorithms
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-031-08720-2

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