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Numerical considerations on decomposition and augmented Lagrangians. (English) Zbl 0982.90051
Nguyen, Van Hien (ed.) et al., Optimization. Proceedings of the 9th Belgian-French-German conference, Namur, Belgium, September 7-11, 1998. Berlin: Springer. Lect. Notes Econ. Math. Syst. 481, 288-304 (2000).
Summary: The authors consider a general large scale constrained minimization problem with separable and differentiable objective function and constraints. The augmented Lagrangian method cannot be directly applied to such a problem because the resulting penalty function is not separable. They first recall two existing approaches (a method based on a linearization of the quadratic term in the augmented Lagrangian) and SALA (for Separable Augmented Lagrangian Algorithm), which is a generalization of proximal decomposition. They also present a new approach based on the decomposition of the line search in primal-dual algorithms, which requires the convexity of the augmented Lagrangian function. They compare the three methods on small and large scale test examples, insisting on robustness in parameter tuning.
For the entire collection see [Zbl 0935.00054].
90C30 Nonlinear programming
49M27 Decomposition methods
49M30 Other numerical methods in calculus of variations (MSC2010)