Analytical target cascading (ATC) is a multidisciplinary design optimization method for multilevel hierarchical systems. To improve computational efficiency, especially for problems under uncertainty or with strong monotonicity, a sequential linear programming (SLP) algorithm was previously employed as an alternate coordination strategy to solve ATC and probabilistic ATC problems. The SLP implementation utilizes norms to maintain the linearity of SLP subsequences. This note offers a proof that there exists a set of weights such that the ATC algorithm converges when norms are used. Examples are also provided to illustrate the effectiveness of using norms as a penalty function to maintain the formulation linear and differentiable. The examples show that the proposed method provides more robust results for linearized ATC problems due to the robustness of the linear programming solver.
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March 2010
Technical Briefs
A Note on the Convergence of Analytical Target Cascading With Infinite Norms
Jeongwoo Han,
e-mail: jhan@anl.gov
Jeongwoo Han
Argonne National Laboratory
, 9700 S. Cass Avenue, Building 362, Argonne, IL 60439
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Panos Y. Papalambros
Panos Y. Papalambros
Department of Mechanical Engineering,
e-mail: pyp@umich.edu
University of Michigan
, 2250 GG Brown Building, Ann Arbor, MI 48104
Search for other works by this author on:
Jeongwoo Han
Argonne National Laboratory
, 9700 S. Cass Avenue, Building 362, Argonne, IL 60439e-mail: jhan@anl.gov
Panos Y. Papalambros
Department of Mechanical Engineering,
University of Michigan
, 2250 GG Brown Building, Ann Arbor, MI 48104e-mail: pyp@umich.edu
J. Mech. Des. Mar 2010, 132(3): 034502 (6 pages)
Published Online: March 1, 2010
Article history
Received:
January 14, 2009
Revised:
December 18, 2009
Online:
March 1, 2010
Published:
March 1, 2010
Citation
Han, J., and Papalambros, P. Y. (March 1, 2010). "A Note on the Convergence of Analytical Target Cascading With Infinite Norms." ASME. J. Mech. Des. March 2010; 132(3): 034502. https://doi.org/10.1115/1.4001001
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