Algencan
Algencan is a software library that implements an Augmented Lagrangian method to solve general nonlinear programming problems. It was introduced by Andreani, Birgin, Martínez, and Schuverdt.[1]. A comprehensive theoretical and practical review of the method, as well as several examples of usage, can be found in the book published by Birgin and Martínez[2]. Complexity results and extensive numerical experiments considering all problems from the CUTEst collection can be found in a recent published paper[3]. Algencan is implemented in Fortran and is freely available at the TANGO project web page.
Algencan is a safeguarded Augmented Lagrangian method in the sense that the estimates of the Lagrange multipliers generated by the method are bounded (this denomination seems to have been coined by Kanzow and Steck[4]). Differently from other methods, Algencan deals with inequality constraints without relying on slack variables. This means that, for a nonlinear programming problem, Algencan computes iterates by solving a subproblem of the form
,
where represents the penalty parameter, and are safeguarded approximations to the Lagrange multipliers associated with equality and inequality constraints, respectively, and
is the augmented Lagrangian function as defined by Michael J. D. Powell[5], Magnus Hestenes[6], and R. Tyrrell Rockafellar[7]
References
- ↑ Andreani, R.; Birgin, E. G.; Martínez, J. M.; Schuverdt, M. L. (2007). "On Augmented Lagrangian methods with general lower-level constraints". SIAM Journal on Optimization. 18 (4): 1286–1309. doi:10.1137/060654797.[permanent dead link]
- ↑ Birgin, E. G.; Martínez, J. M. (2014). Practical Augmented Lagrangian Methods for Constrained Optimization. Philadelphia: Society for Industrial and Applied Mathematics. ISBN 978-1-611973-35-8. Search this book on
- ↑ Birgin, E. G.; Martínez, J. M. (2020). "Complexity and performance of an Augmented Lagrangian algorithm". Optimization Methods and Software. 35 (5): 885–920. arXiv:1907.02401. doi:10.1080/10556788.2020.1746962. Unknown parameter
|s2cid=ignored (help) - ↑ Kanzow, C.; Steck, D. (2017). "An example comparing the standard and safeguarded augmented Lagrangian methods". Operations Research Letters. 45 (6): 598–603. doi:10.1016/j.orl.2017.09.005.
- ↑ Powell, M. J. D. (1969). "A method for nonlinear constraints in minimization problems". In Fletcher, R. Optimization. New York, NY: Academic Press. pp. 283–298. Search this book on
- ↑ Hestenes, M. R. (1969). "Multiplier and gradient methods". Journal of Optimization Theory and Applications. 4 (5): 303–320. doi:10.1007/BF00927673. Unknown parameter
|s2cid=ignored (help) - ↑ Rockafellar, R. T. (1974). "Augmented Lagrange multiplier functions and duality in nonconvex programming". SIAM Journal on Control and Optimization. 12 (2): 268–285. doi:10.1137/0312021.
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