Addressing the greediness phenomenon in Nonlinear Programming by means of Proximal Augmented Lagrangians

When one solves Nonlinear Programming problems by means of algorithms that use merit criteria combining the objective function and penalty feasibility terms, a phenomenon called greediness may occur. Unconstrained minimizers attract the iterates at early stages of the calculations and, so, the penal...

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Bibliographic Details
Published in:Computational optimization and applications 2010-06, Vol.46 (2), p.229-245
Main Authors: Castelani, Emerson V., Martinez, André L. M., Martínez, J. M., Svaiter, B. F.
Format: Article
Language:English
Subjects:
Algorithms
Applied mathematics
Convex and Discrete Geometry
Management Science
Mathematics
Mathematics and Statistics
Nonlinear programming
Operations Research
Operations Research/Decision Theory
Optimization
Statistics
Studies
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Summary:When one solves Nonlinear Programming problems by means of algorithms that use merit criteria combining the objective function and penalty feasibility terms, a phenomenon called greediness may occur. Unconstrained minimizers attract the iterates at early stages of the calculations and, so, the penalty parameter needs to grow excessively, in such a way that ill-conditioning harms the overall convergence. In this paper a regularization approach is suggested to overcome this difficulty. An Augmented Lagrangian method is defined with the addition of a regularization term that inhibits the possibility that the iterates go far from a reference point. Convergence proofs and numerical examples are given.
ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-009-9271-4