Modern Numerical Nonlinear Optimization

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.

Nonlinear optimization algorithms for solving large-scale unconstrained and constrained optimization applications Optimization methods that are currently the most valuable for solving real-life problems and applications Provides theoretical background which gives insights into how the methods are derived

Auteur

Neculai Andrei holds a position at the Center for Advanced Modeling and Optimization at the Academy of Romanian Scientists in Bucharest, Romania. Dr. Andrei s areas of interest include mathematical modeling, linear programming, nonlinear optimization, high performance computing, and numerical methods in mathematical programming. In addition to this present volume, Neculai Andrei has published several books with Springer including A Derivative-free Two Level Random Search Method for Unconstrained Optimization (2021), Nonlinear Conjugate Gradient Methods for Unconstrained Optimization (2020), Continuous Nonlinear Optimization for Engineering Applications in GAMS Technology (2017), and Nonlinear Optimization Applications Using the GAMS Technology (2013).

Résumé
"This book gives a comprehensive description of the theoretical details and the computational performance of the modern optimization algorithms for solving ... different areas of activity. ... I think this book has the following two features. First, it emphasizes and illustrates a number of reliable and robust packages for solving ... nonlinear optimization problems and applications. Second, the text is well illustrated with drawings and numerical studies of many large-scale test problems, which significantly increase the readability of the book." (Xiaoliang Dong, Mathematical Reviews, September, 2023)

Contenu

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.