Global minimization using an Augmented Lagrangian method with variable lower-level constraints

A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration k the method requires the -global minimization of the Augmented Lagrangian with simple constraints, where . Global convergen...

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Bibliographic Details
Published in:Mathematical programming 2010-09, Vol.125 (1), p.139-162
Main Authors: Birgin, E. G., Floudas, C. A., Martínez, J. M.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Calculus of variations and optimal control
Calculus of Variations and Optimal Control
Optimization
Combinatorics
Constraints
Convergence
Exact sciences and technology
Full Length Paper
Iterative methods
Lagrange multiplier
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical models
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Minimization
Nonlinearity
Numerical Analysis
Operational research and scientific management
Operational research. Management science
Optimization
Optimization techniques
Parameter estimation
Sciences and techniques of general use
Theoretical
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Summary:A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration k the method requires the -global minimization of the Augmented Lagrangian with simple constraints, where . Global convergence to an -global minimizer of the original problem is proved. The subproblems are solved using the α BB method. Numerical experiments are presented.
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-009-0264-y