Augmented Lagrangian techniques for the solution of practical constrained optimization problems are the focus of this book, which gives a thorough account of both theory and applications. The authors rigorously delineate mathematical convergence theory based on sequential optimality conditions and novel constraint qualifications. They also orient the book to practitioners by prioritizing results that provide insight on the practical behavior of algorithms and by providing geometrical and algorithmic interpretations of every mathematical result. In addition, they fully describe a freely available computational package for constrained optimization and illustrate its usefulness with applications. This 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.
Ernesto Birgin is a professor in the Department of Computer Science at the Institute of Mathematics and Statistics of the University of Sao Paulo. He is a member of the editorial boards of the Journal of Global Optimization, Computational and Applied Mathematics, the Bulletin of Computational Applied Mathematics, Pesquisa Operacional, and Trends in Applied and Computational Mathematics. He has published over 50 papers on computational optimization and applications. Jose Mario Martinez is a professor in the Department of Applied Mathematics at the University of Campinas, Brazil. He is a member of the Brazilian Academy of Sciences, former Editor in Chief of Computational and Applied Mathematics, a member of the editorial board of Numerical Algorithms, and the author of over 150 papers on numerical mathematics, optimization, and applications.
Preface; Nomenclature; 1. Introduction; 2. Practical motivations; 3. Optimality conditions; 4. Model augmented Lagrangian algorithm; 5. Global minimization approach; 6. General affordable algorithms; 7. Boundedness of the penalty parameters; 8. Solving unconstrained subproblems; 9. Solving constrained subproblems; 10. First approach to Algencan; 11. Adequate choice of subroutines; 12. Making a good choice of algorithmic options and parameters; 13. Practical examples; 14. Final remarks; Bibliography; Author index; Subject index.
A guide to augmented Lagrangian techniques for optimization problems which emphasises algorithms and computation alongside theory.
