Brazilian mathematicians explain the augmented Lagrangian method for solving constrained optimization problems for engineers, chemists, physicists, economists, and others who use constrained optimization for solving real-life problems. They assume readers are familiar with elementary calculus in Rn with the basic topological properties concerning convergence of sequences and compact sets, but no further mathematical background. After the statement and interpretation of all the relevant theory, they introduce a specific constrained optimization package of augmented Lagrangian type called Algencan. Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)
A guide to augmented Lagrangian techniques for optimization problems which emphasises algorithms and computation alongside theory.
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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
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.
