Modified augmented Lagrangian coordination and alternating direction method of multipliers with parallelization in non-hierarchical analytical target cascading

Analytical target cascading (ATC), a hierarchical, multilevel, multidisciplinary coordination method, has proven to be an effective decomposition approach for large-scale engineering optimization problems. In recent years, augmented Lagrangian relaxation methods have received renewed interest as dual update methods for solving ATC decomposed problems. These problems can be solved using the subgradient optimization algorithm, the application of which includes three schemes for updating dual variables. To address the convergence efficiency disadvantages of the existing dual update schemes, this paper investigates two new schemes, the linear and the proximal cutting plane methods, which are implemented in conjunction with augmented Lagrangian coordination for ATC-decomposed problems. Three nonconvex nonlinear example problems are used to show that these two cutting plane methods can significantly reduce the number of iterations and the number of function evaluations when compared to the traditional subgradient update methods. In addition, these methods are also compared to the method of multipliers and its variants, showing similar performance.

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Improving the Performance of the Augmented Lagrangian Coordination: Decomposition Variants and Dual Residuals

Journal of Mechanical Design ◽

10.1115/1.4035501 ◽

2017 ◽

Vol 139 (3) ◽

Cited By ~ 2

Author(s):

Meng Xu ◽

Georges Fadel ◽

Margaret M. Wiecek

Keyword(s):

Test Problem ◽

Augmented Lagrangian ◽

Analytical Target Cascading ◽

Advantages And Disadvantages ◽

Numerical Tests ◽

Target Cascading ◽

Augmented Lagrangian Coordination

The augmented Lagrangian coordination (ALC), as an effective coordination method for decomposition-based optimization, offers significant flexibility by providing different variants when solving nonhierarchically decomposed problems. In this paper, these ALC variants are analyzed with respect to the number of levels and multipliers, and the resulting advantages and disadvantages are explored through numerical tests. The efficiency, accuracy, and parallelism of three ALC variants (distributed ALC, centralized ALC, and analytical target cascading (ATC) extended by ALC) are discussed and compared. Furthermore, the dual residual theory for the centralized ALC is extended to the distributed ALC, and a new flexible nonmonotone weight update is proposed and tested. Numerical tests show that the proposed update effectively improves the accuracy and robustness of the distributed ALC on a benchmark engineering test problem.

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L1-Norm Least Squares Support Vector Regression via the Alternating Direction Method of Multipliers

Journal of Advanced Computational Intelligence and Intelligent Informatics ◽

10.20965/jaciii.2017.p1017 ◽

2017 ◽

Vol 21 (6) ◽

pp. 1017-1025

Author(s):

Ya-Fen Ye ◽

Chao Ying ◽

Yue-Xiang Jiang ◽

Chun-Na Li ◽

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...

Keyword(s):

Feature Selection ◽

Least Squares ◽

Support Vector Regression ◽

Augmented Lagrangian ◽

Alternating Direction Method ◽

Support Vector ◽

Method Of Multipliers ◽

L1 Norm ◽

Feature Selection Problem ◽

Alternating Direction

In this study, we focus on the feature selection problem in regression, and propose a new version of L1support vector regression (L1-SVR), known as L1-norm least squares support vector regression (L1-LSSVR). The alternating direction method of multipliers (ADMM), a method from the augmented Lagrangian family, is used to solve L1-LSSVR. The sparse solution of L1-LSSVR can realize feature selection effectively. Furthermore, L1-LSSVR is decomposed into a sequence of simpler problems by the ADMM algorithm, resulting in faster training speed. The experimental results demonstrate that L1-LSSVR is not only as effective as L1-SVR, LSSVR, and SVR in both feature selection and regression, but also much faster than L1-SVR and SVR.

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