Modern Numerical Nonlinear Optimization

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).

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 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)

“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)