Modern numerical nonlinear optimization (Q2160137)

The book deals with nonlinear optimization with emphasis on solving large-scale problems, which have a real-world application. The book is divided into two main parts. The first part containing the first nine chapters is devoted to theoretical and practical aspects of unconstraint nonlinear optimization. The second part of the book (Chapters 10--20) studies solution methods appropriate for constrained nonlinear optimization problems. Special attention is devoted to optimality conditions, especially to KKT-conditions (Kuhn-Karush-Tucker optimality conditions) characterizing local optimal solutions of nonlinear optimization problems. These theoretical chapters (Chapters 10--11) are followed by a detailed description of solution methods. The methods for unconstraint problems are based mainly on two ideas, namely the line-search and trust region. The constrained nonlinear optimization methods considered in this book are mainly based on penalty and augmented Lagragian, the sequential quadratic programming, the generalized reduced gradient, the interior point, the filter methods and the direct search methods which do not use the derivative information. Some of the methods combine these strategies. Since the optimization problems are supposed to be large-scale, the author provides the readers with slected reliable and robust packages designed for solving large-scale uncostraint and constraint non-linear optimization problems. The main text of the book is followed by four appendices, which serve to facilitating of understanding the theoretical chapters of the book (Appendix A) and to informing about behavior of the considered optimization methods when they are applied to practical problems (Appendices B,C,D).