An augmented Lagrangian relaxation for analytical target cascading using the alternating direction method of multipliers |
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Authors: | S Tosserams L F P Etman P Y Papalambros J E Rooda |
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Affiliation: | (1) Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;(2) Department of Mechanical Engineering, The University of Michigan, 2250 GG Brown Building, Ann Arbor, MI 48104-2125, USA |
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Abstract: | Analytical target cascading is a method for design optimization of hierarchical, multilevel systems. A quadratic penalty relaxation
of the system consistency constraints is used to ensure subproblem feasibility. A typical nested solution strategy consists
of inner and outer loops. In the inner loop, the coupled subproblems are solved iteratively with fixed penalty weights. After
convergence of the inner loop, the outer loop updates the penalty weights. The article presents an augmented Lagrangian relaxation
that reduces the computational cost associated with ill-conditioning of subproblems in the inner loop. The alternating direction
method of multipliers is used to update penalty parameters after a single inner loop iteration, so that subproblems need to
be solved only once. Experiments with four examples show that computational costs are decreased by orders of magnitude ranging
between 10 and 1000. |
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Keywords: | Multidisciplinary optimization Decomposition Analytical target cascading Augmented Lagrangian relaxation Penalty functions |
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