Dislocation hyperbolic augmented Lagrangian algorithm in convex programming

Authors

DOI:

https://doi.org/10.11121/ijocta.1402

Keywords:

Augmented Lagrangian, constrained optimization, convergence, convex problem

Abstract

The dislocation hyperbolic augmented Lagrangian algorithm (DHALA) is a new approach to the hyperbolic augmented Lagrangian algorithm (HALA). DHALA is designed to solve convex nonlinear programming problems. We guarantee that the sequence generated by DHALA converges towards a Karush-Kuhn-Tucker point. We are going to observe that DHALA has a slight computational advantage in solving the problems over HALA. Finally, we will computationally illustrate our theoretical results.

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Author Biographies

Lennin Mallma Ramirez, Federal University of Rio de Janeiro, Systems Engineering and Computer Science Program (COPPE), Rio de Janeiro, Brazil

Lennin Mallma Ramirez received his Ph.D degrees in PESC/COPPE/UFRJ, Brazil (2022). He was a visiting research at the ICTEAM/UCLouvain, Belgium.nHe is currently doing a Postdoc in PESC/COPPE/UFRJ, Rio de Janeiro, Brazil. He is interested in researching continuous optimization algorithms.

Nelson Maculan, Federal University of Rio de Janeiro, Systems Engineering and Computer Science Program-Applied Mathematics (IM/COPPE), Rio de Janeiro, Brazil

Nelson Maculan Professor Emeritus Federal University of Rio de Janeiro, DHR Management Sciences, University of Paris-Dauphine, PhD Production Engineering, Federal University of Rio de Janeiro. Editor in Chief of RAIRO Operations Research journal.

Adilson Elias Xavier, Federal University of Rio de Janeiro, Systems Engineering and Computer Science Program (COPPE), Rio de Janeiro, Brazil

Adilson Elias Xavier received his Ph.D degrees in PESC/COPPE/UFRJ, Brazil (1992). He is a professor at PESC/COPPE/UFRJ, Brazil. Working mainly on the following topics: Hyperbolic Penalty, Optimization, Nonlinear Programming, Multiplier Methods.

Vinicius Layter Xavier, Rio de Janeiro State University, Institute of Mathematics and Statistics, Graduate Program in Computational Sciences, Rio de Janeiro, Brazil

Vinicius Layter Xavier received his Ph.D degrees in PESC/COPPE/UFRJ, Brazil (2016). He is a professor at the IME/UERJ, Rio de Janeiro, Brazil. Working mainly on the following topics: Multivariate Statistics, Cluster Analysis, Nondifferentiable Programming, Min-Sum-Min Problems, Statistical Learning and Pattern Recognition.

References

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Published

2024-04-07
CITATION
DOI: 10.11121/ijocta.1402
Published: 2024-04-07

How to Cite

Mallma Ramirez, L., Maculan, N. ., Elias Xavier, A., & Layter Xavier, V. (2024). Dislocation hyperbolic augmented Lagrangian algorithm in convex programming. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 14(2), 147–155. https://doi.org/10.11121/ijocta.1402

Issue

Vol. 14 No. 2 (2024): IJOCTA

Section

Research Articles

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Copyright (c) 2024 Lennin Mallma Ramirez, Nelson Maculan, Adilson Elias Xavier, Vinicius Layter Xavier

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