Modern numerical nonlinear optimization 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.