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Research Papers

A Regularized Inexact Penalty Decomposition Algorithm for Multidisciplinary Design Optimization Problems With Complementarity Constraints

[+] Author and Article Information
Shen Lu

Department of Industrial and Enterprise Systems Engineering, University of Illinois, Urbana, IL 61801shenlu2@illinois.edu

Harrison M. Kim

Department of Industrial and Enterprise Systems Engineering, University of Illinois, Urbana, IL 61801hmkim@illinois.edu

A feasible point x of an MPCC is Bouligard stationary (B-stationary) if it is a local minimizer of the linearized MPCC, which is obtained by linearizing all data functions at point x(40).

J. Mech. Des 132(4), 041005 (Apr 13, 2010) (12 pages) doi:10.1115/1.4001206 History: Received April 14, 2009; Revised January 29, 2010; Published April 13, 2010; Online April 13, 2010

Economic and physical considerations often lead to equilibrium problems in multidisciplinary design optimization (MDO), which can be captured by MDO problems with complementarity constraints (MDO-CC)—a newly emerging class of problem. Due to the ill-posedness associated with the complementarity constraints, many existing MDO methods may have numerical difficulties solving this class of problem. In this paper, we propose a new decomposition algorithm for the MDO-CC based on the regularization technique and inexact penalty decomposition. The algorithm is presented such that existing proofs can be extended, under certain assumptions, to show that it converges to stationary points of the original problem and that it converges locally at a superlinear rate. Numerical computation with an engineering design example and several analytical example problems shows promising results with convergence to the all-in-one solution.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

The flow of formulation manipulation and stationary point mapping

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Figure 2

The feasible space of 0≤[Gi]j⊥[Fi]j≥0 and its regularization (7) (a and b)

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Figure 3

The nested loop framework of the regularized IPD algorithm

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Figure 4

The single loop framework of the regularized IPD algorithm

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Figure 5

The BFGS procedure

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Figure 6

An illustration of the convergence procedure (a and b)

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Figure 7

A schematic of the Golinski’s speed reducer

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Figure 8

Numerical behavior of the RIPD approach compared with the augmented Lagrangian decomposition (7)

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