Augmented Lagrangian Method for Linear Programming Using Smooth Approximation

Hossein Moosaei; Saeed Ketabchi; Mujahid N. Syed; Fatemeh Bazikar

doi:10.1007/978-3-031-50320-7_13

Augmented Lagrangian Method for Linear Programming Using Smooth Approximation

Hossein Moosaei^*
, Saeed Ketabchi
, Mujahid N. Syed
, Fatemeh Bazikar

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The augmented Lagrangian method can be used for finding the least 2 - norm solution of a linear programming problem. This approach’s primary advantage is that it leads to the minimization of an unconstrained problem with a piecewise quadratic, convex, and differentiable objective function. However, this function lacks an ordinary Hessian, which precludes the use of a fast Newton method. In this paper, we apply the smoothing techniques and solve an unconstrained smooth reformulation of this problem using a fast Newton method. Computational results and comparisons are illustrated through multiple numerical examples to show the effectiveness of the proposed algorithm.

Original language	English
Title of host publication	Dynamics of Information Systems - 6th International Conference, DIS 2023, Revised Selected Papers
Editors	Hossein Moosaei, Milan Hladík, Panos M. Pardalos
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	186-193
Number of pages	8
ISBN (Print)	9783031503191
DOIs	https://doi.org/10.1007/978-3-031-50320-7_13
State	Published - 2024
Event	6th International Conference on Dynamics of Information Systems, DIS 2023 - Prague, Czech Republic Duration: 3 Sep 2023 → 6 Sep 2023

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	14321 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	6th International Conference on Dynamics of Information Systems, DIS 2023
Country/Territory	Czech Republic
City	Prague
Period	3/09/23 → 6/09/23

Bibliographical note

Publisher Copyright:
© 2024, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Keywords

Augmented Lagrangian method
Generalized Newton method
Smooth approximation

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-031-50320-7_13

Cite this

Moosaei, H., Ketabchi, S., Syed, M. N., & Bazikar, F. (2024). Augmented Lagrangian Method for Linear Programming Using Smooth Approximation. In H. Moosaei, M. Hladík, & P. M. Pardalos (Eds.), Dynamics of Information Systems - 6th International Conference, DIS 2023, Revised Selected Papers (pp. 186-193). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14321 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-50320-7_13

Moosaei, Hossein ; Ketabchi, Saeed ; Syed, Mujahid N. et al. / Augmented Lagrangian Method for Linear Programming Using Smooth Approximation. Dynamics of Information Systems - 6th International Conference, DIS 2023, Revised Selected Papers. editor / Hossein Moosaei ; Milan Hladík ; Panos M. Pardalos. Springer Science and Business Media Deutschland GmbH, 2024. pp. 186-193 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "The augmented Lagrangian method can be used for finding the least 2 - norm solution of a linear programming problem. This approach{\textquoteright}s primary advantage is that it leads to the minimization of an unconstrained problem with a piecewise quadratic, convex, and differentiable objective function. However, this function lacks an ordinary Hessian, which precludes the use of a fast Newton method. In this paper, we apply the smoothing techniques and solve an unconstrained smooth reformulation of this problem using a fast Newton method. Computational results and comparisons are illustrated through multiple numerical examples to show the effectiveness of the proposed algorithm.",

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Moosaei, H, Ketabchi, S, Syed, MN & Bazikar, F 2024, Augmented Lagrangian Method for Linear Programming Using Smooth Approximation. in H Moosaei, M Hladík & PM Pardalos (eds), Dynamics of Information Systems - 6th International Conference, DIS 2023, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 14321 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 186-193, 6th International Conference on Dynamics of Information Systems, DIS 2023, Prague, Czech Republic, 3/09/23. https://doi.org/10.1007/978-3-031-50320-7_13

Augmented Lagrangian Method for Linear Programming Using Smooth Approximation. / Moosaei, Hossein; Ketabchi, Saeed; Syed, Mujahid N. et al.
Dynamics of Information Systems - 6th International Conference, DIS 2023, Revised Selected Papers. ed. / Hossein Moosaei; Milan Hladík; Panos M. Pardalos. Springer Science and Business Media Deutschland GmbH, 2024. p. 186-193 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14321 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - The augmented Lagrangian method can be used for finding the least 2 - norm solution of a linear programming problem. This approach’s primary advantage is that it leads to the minimization of an unconstrained problem with a piecewise quadratic, convex, and differentiable objective function. However, this function lacks an ordinary Hessian, which precludes the use of a fast Newton method. In this paper, we apply the smoothing techniques and solve an unconstrained smooth reformulation of this problem using a fast Newton method. Computational results and comparisons are illustrated through multiple numerical examples to show the effectiveness of the proposed algorithm.

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Moosaei H, Ketabchi S, Syed MN, Bazikar F. Augmented Lagrangian Method for Linear Programming Using Smooth Approximation. In Moosaei H, Hladík M, Pardalos PM, editors, Dynamics of Information Systems - 6th International Conference, DIS 2023, Revised Selected Papers. Springer Science and Business Media Deutschland GmbH. 2024. p. 186-193. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-50320-7_13