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

Shen Lu

,
Shen Lu

Department of Industrial and Enterprise Systems Engineering,

shenlu2@illinois.edu
University of Illinois

, Urbana, IL 61801
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Harrison M. Kim

Harrison M. Kim

Department of Industrial and Enterprise Systems Engineering,

hmkim@illinois.edu
University of Illinois

, Urbana, IL 61801
Search for other works by this author on:

Shen Lu

Department of Industrial and Enterprise Systems Engineering,

University of Illinois

, Urbana, IL 61801shenlu2@illinois.edu

Harrison M. Kim

University of Illinois

, Urbana, IL 61801hmkim@illinois.edu

*J. Mech. Des*. Apr 2010, 132(4): 041005 (12 pages)

**Published Online:**April 13, 2010

Article history

Received:

April 14, 2009

Revised:

January 29, 2010

Online:

April 13, 2010

Published:

April 13, 2010

Citation

Lu, S., and Kim, H. M. (April 13, 2010). "A Regularized Inexact Penalty Decomposition Algorithm for Multidisciplinary Design Optimization Problems With Complementarity Constraints." ASME. *J. Mech. Des*. April 2010; 132(4): 041005. https://doi.org/10.1115/1.4001206

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