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Mathematics > Numerical Analysis

arXiv:1804.08072 (math)
[Submitted on 22 Apr 2018]

Title:Modified Augmented Lagrangian Method for the minimization of functions with quadratic penalty terms

Authors:Martin Neuenhofen
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Abstract:The Augmented Lagrangian Method (ALM) is an iterative method for the solution of equality-constrained non-linear programming problems. In contrast to the quadratic penalty method, the ALM can satisfy equality constraints in an exact way. Further, ALM is claimed to converge in less iterations, indicating that it is superior in approach to a quadratic penalty method.
It is referred to as an advantage that the ALM solves equality constraints in an exact way, meaning that the penalty parameter does not need to go to infinity in order to yield accurate feasibility for the constraints. However, we sometimes actually want to minimize an unconstrained problem that has large quadratic penalty terms. In these situations it is unclear how the ALM could be utilized in the correct way. This paper presents the answer: We derive a modified version of the ALM that is also suitable for solving functions with large quadratic penalty terms.
Comments: 13 pages
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:1804.08072 [math.NA]
  (or arXiv:1804.08072v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1804.08072

Submission history

From: Martin Peter Neuenhofen [view email]
[v1] Sun, 22 Apr 2018 06:21:59 UTC (13 KB)
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