Modern Numerical Nonlinear Optimization

Beschreibung

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.

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.

Autor*in

Neculai Andrei

Themen in »Modern Numerical Nonlinear Optimization«

unconstrained optimization stepsize computation steepest descent method Newton method conjugate gradient method quasi-Newton methods inexact Newton method trust-region method constrained nonlinear optimization simple bound optimization quadratic programming augmented Lagrangian penalty Lagrangian sequential quadratic programming Interior-point methods

Stimmen zu »Modern Numerical Nonlinear Optimization«

“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)
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