This book focuses on Augmented Lagrangian techniques for solving practical constrained optimization problems. The authors rigorously delineate mathematical convergence theory based on sequential optimality conditions and novel constraint qualifications. They also orient the book to practitioners by giving priority to results that provide insight on the practical behavior of algorithms and by providing geometrical and algorithmic interpretations of every mathematical result, and they fully describe a freely available computational package for constrained optimization and illustrate its usefulness with applications.
Audience: The book is aimed at engineers, physicists, chemists, and other practitioners interested in full access to comprehensive and well-documented software for large-scale optimization as well as up-to-date convergence theory and its practical consequences. It will also be of interest to graduate and advanced undergraduate students in mathematics, computer science, applied mathematics, optimization, and numerical analysis.
Contents: Chapter 1: Introduction ; Chapter 2: Practical Motivations; Chapter 3: Optimality Conditions; Chapter 4: Model Augmented Lagrangian Algorithm; Chapter 5: Global Minimization Approach; Chapter 6: General Affordable Algorithms; Chapter 7: Boundedness of the Penalty Parameters; Chapter 8: Solving Unconstrained Subproblems; Chapter 9: Solving Constrained Subproblems; Chapter 10: First Approach to Algencan; Chapter 11: Adequate Choice of Subroutines; Chapter 12: Making a Good Choice of Algorithmic Options and Parameters; Chapter 13: Practical Examples; Chapter 14: Final Remarks