KSME International Journal

, Volume 14, Issue 10, pp 1122–1130 | Cite as

A new penalty parameter update rule in the augmented lagrange multiplier method for dynamic response optimization

Materials & Fracture · Solids & Structures · Dynamics & Control · Production & Design

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.

Key Words

Penalty Parameter Augmented Lagrange Multiplier Method Dynamic Response Optimization 

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References

  1. 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.MATHCrossRefMathSciNetGoogle Scholar
  2. 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.CrossRefGoogle Scholar
  3. Gill, P. E., Murray, W. and Wright, M. H., 1981,Practical Optimization, Academic Press, Inc., pp. 225–230.Google Scholar
  4. Haug F. J. and Arora, J. S., 1979,Applied Optimal Design, Wlley-Interscience, New York, pp. l78–2l2.Google Scholar
  5. 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.MATHCrossRefGoogle Scholar
  6. 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.MATHCrossRefGoogle Scholar
  7. 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.CrossRefGoogle Scholar
  8. Kim, M. -S., 1997,Dynamic Response Optimization Using the Augmented Lagrange Multiplier Menthod and Approximation Techniques, Ph. D. Thesis, Hanyang University.Google Scholar
  9. 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.Google Scholar
  10. 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).Google Scholar
  11. Luenberger, D. G., 1984,Linear and Nonlinear Programming, 2nd Eds,, Addison-Wesley, Reeding, MA, pp. 406–4l5.MATHGoogle Scholar
  12. 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.CrossRefGoogle Scholar
  13. 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.CrossRefMathSciNetGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers (KSME) 2000

Authors and Affiliations

  1. 1.BK2I Division for Research and Education in Mechanical EngineeringHanyang UniversityKorea

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