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J. B. Lassiter, M. M. Wiecek and K. R. Andrighetti, “Lagrangian Coordination and Analytical Target Cascading: Solving ATC-Decomposed Problems with LagrangianDuality,” Optimization and Engineering, Vol. 6, No. 3, 2005, pp. 361-381. doi:10.1007/s11081-005-1744-4

has been cited by the following article:

• TITLE: Comparison of Alternative Strategies for Multilevel Optimization of Hierarchical Systems

  AUTHORS: Saber DorMohammadi, Masoud Rais-Rohani

  KEYWORDS: Analytical Target Cascading; Multilevel Design Optimization; Augmented Lagrangian; Method of Multipliers

  JOURNAL NAME: Applied Mathematics, Vol.3 No.10A, November 1, 2012

  ABSTRACT: The augmented Lagrangian penalty formulation and four different coordination strategies are used to examine the nu- merical behavior of Analytical Target Cascading (ATC) for multilevel optimization of hierarchical systems. The coordination strategies considered include augmented Lagrangian using the method of multipliers and alternating direction method of multipliers, diagonal quadratic approximation, and truncated diagonal quadratic approximation. Properties examined include computational cost and solution accuracy based on the selected values for the different parameters that appear in each formulation. The different strategies are implemented using two- and three-level decomposed example problems. While the results show the interaction between the selected ATC formulation and the values of associated parameters, they clearly highlight the impact they could have on both the solution accuracy and computational cost.