Abstract
Based on the value of the Lagrange multiplier and the degree of constraint activeness, a new update rule is proposed for penalty parameters of the ALM method. The theoretical exposition of this suggested update rule is presented by using the algorithmic interpretation and the geometric interpretation of the augmented Lagrangian. This interpretation shows that the penalty parameters can effect the performance of the ALM method. Also, it offers a lower limit on the penalty parameters that makes the augmented Lagrangian to be bounded. This lower limit forms the backbone of the proposed update rule. To investigate the numerical performance of the update rule, it is embedded in our ALM based dynamic response optimizer, and the optimizer is applied to solve six typical dynamic response optimization problems. Our optimization results are compared with those obtained by employing three conventional update rules used in the literature, which shows that the suggested update rule is more efficient and more stable than the conventional ones.
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References
Arora, J. S., Chahande, A. I. and Paeng, J. K., 1991, “Multiplier Methods for Engineering Optimization,”Int. J. Numer. Meth. Engng., Vol, 32, pp. 1485–1525.
Chahande, A. I. and Arora, J. S., 1994, “Optimization of Large Structures subjected to Dynamic Loads with the Multiplier method,”Int. J. Numer. Meth. Engng., Vol, 37, pp. 4l3–430.
Gill, P. E., Murray, W. and Wright, M. H., 1981,Practical Optimization, Academic Press, Inc., pp. 225–230.
Haug F. J. and Arora, J. S., 1979,Applied Optimal Design, Wlley-Interscience, New York, pp. l78–2l2.
Hsieh, C. C. and Arora, J. S., 1984, “Design Sensitivity Analysis and Optimization of Dynamic Response,”Comput. Meth. Appl Mech. Engng., Vol, 43, pp. 195–2l9.
Hsieh, C. C. and Arora, J. S., 1985, “Hybrid Formulation for treatment of Point-wise State Variable Constraints in Dynamic Response Optimization,”Comput. Meth. Appl. Mech. Engng., Vol, 48, pp. 171–189.
Kim, M. -S. and Choi, D.-H. 1988, “Min-Max Dynamic Response Optimization of Mechanical Systems Using Approximate Augmented Lagrangian,”Int. J. Numer. Meth. Engng., Vol. 43, pp. 549–564.
Kim, M. -S., 1997,Dynamic Response Optimization Using the Augmented Lagrange Multiplier Menthod and Approximation Techniques, Ph. D. Thesis, Hanyang University.
Kim, M. -S. and Choi, D. -H., 1995, “A Development of Efficient Line Search by Using Sequential polynomial Approximations,”KSME (in Korean) , Vol. 19, No. 2, pp. 433–442.
Kim, M. -S. and Choi, D. -H. 2001, “Direct Treatment of Max-Value Cost Function in Parametric Optimization,”Int. J. Numer. Meth. Engng., (to be published).
Luenberger, D. G., 1984,Linear and Nonlinear Programming, 2nd Eds,, Addison-Wesley, Reeding, MA, pp. 406–4l5.
Paeng, J. K. and Arora, J. S., 1989, “Dynamic Response Optimization of Mechanical Systems with Multiplier Methods,”ASME.1. Mechanism, Transmission, and Automat. Des., Vol, 111, pp. 73–80.
Rockafeller, R. T., 1973, “The Multiplier Method of Hestenes and Powell Applied to Convex programming,”Journal of Optimization Theory and Applications, Vol, 12, No. 6, pp. 555–562.
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Kim, MS., Choi, DH. A new penalty parameter update rule in the augmented lagrange multiplier method for dynamic response optimization. KSME International Journal 14, 1122–1130 (2000). https://doi.org/10.1007/BF03185066
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DOI: https://doi.org/10.1007/BF03185066