Safeguarded augmented Lagrangian algorithms with scaled stopping criterion for the subproblems

E. G. Birgin (), G. Haeser () and J. M. Martínez ()
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E. G. Birgin: University of São Paulo
G. Haeser: University of São Paulo
J. M. Martínez: University of Campinas

Computational Optimization and Applications, 2025, vol. 91, issue 2, No 6, 509 pages

Abstract: Abstract At each iteration of the safeguarded augmented Lagrangian algorithm Algencan, a bound-constrained subproblem consisting of the minimization of the Powell–Hestenes–Rockafellar augmented Lagrangian function is considered, for which an approximate minimizer with tolerance tending to zero is sought. More precisely, a point that satisfies a subproblem first-order necessary optimality condition with tolerance tending to zero is required. In this work, based on the success of scaled stopping criteria in constrained optimization, we propose a scaled stopping criterion for the subproblems of Algencan. The scaling is done with the maximum absolute value of the first-order Lagrange multipliers approximation, whenever it is larger than one. The difference between the convergence theory of the scaled and non-scaled versions of Algencan is discussed and extensive numerical experiments are provided.

Keywords: Nonlinear optimization; Augmented Lagrangian methods; Subproblems; Scaled stopping criteria; Convergence (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10589-024-00572-w

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