An adaptive augmented Lagrangian method for large-scale constrained optimization

We propose an augmented Lagrangian algorithm for solving large-scale constrained optimization problems. The novel feature of the algorithm is an adaptive update for the penalty parameter motivated by recently proposed techniques for exact penalty methods. This adaptive updating scheme greatly improv...

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Bibliographic Details
Published in:Mathematical programming Vol. 152; no. 1-2; pp. 201 - 245
Main Authors: Curtis, Frank E., Jiang, Hao, Robinson, Daniel P.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2015
Springer Nature B.V
Subjects:
Adaptive algorithms
Algorithms
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Constraints
Convergence
Full Length Paper
Lagrange multiplier
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical models
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Methods
Numerical Analysis
Optimization
Studies
Theoretical
Steering methods
65K15
Nonconvex optimization
65K05
Nonlinear optimization
Augmented Lagrangians
90C06
Matrix-free methods
90C30
49M29
65K10
Large-scale optimization
49M05
49M15
49M37
93B40
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary:We propose an augmented Lagrangian algorithm for solving large-scale constrained optimization problems. The novel feature of the algorithm is an adaptive update for the penalty parameter motivated by recently proposed techniques for exact penalty methods. This adaptive updating scheme greatly improves the overall performance of the algorithm without sacrificing the strengths of the core augmented Lagrangian framework, such as its ability to be implemented matrix-free. This is important as this feature of augmented Lagrangian methods is responsible for renewed interests in employing such methods for solving large-scale problems. We provide convergence results from remote starting points and illustrate by a set of numerical experiments that our method outperforms traditional augmented Lagrangian methods in terms of critical performance measures.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-014-0784-y