Duality in convex nonlinear multipoint approximations with diagonal approximate hessian matrices deriving from incomplete series expansions

Collection of Technical Papers - 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

Volumn 4, Issue , 2006, Pages 2151-2173

  Groenwold, Albert A ^a   Etman, L F P ^b  

^a STELLENBOSCH UNIVERSITY   (South Africa)

^b EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; CONSTRAINT THEORY; MATRIX ALGEBRA; OPTIMIZATION; PROBLEM SOLVING; TOPOLOGY;

INCOMPLETE SERIES EXPANSION (ISE); METHOD OF MOVING ASYMPTOTES (MMA); NONLINEAR MULTIPOINT APPROXIMATIONS; SEQUENTIAL APPROXIMATE OPTIMIZATION (SAO);

APPROXIMATION THEORY;

EID: 33846543260     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (35)

1. K. Svanberg. The method of moving asymptotes - a new method for structural optimization. Int. J. Numer. Meth Eng., 24:359-373, 1987.
2. K. Svanberg. A globally convergent version of MMA without linesearch. In G.I.N. Rozvany and N. Olhoff, editors, Proc. First World Congress on Structural and Multidisciplinary Optimization, pages 9-16, Goslar, Germany, 1995.
3. C. Fleury and V. Braibant. Structural optimization: a new dual method using mixed variables. Int. J. Numer. Meth. Eng., 23:409-428, 1986.
4. G.M. Fadel, M.F. Riley, and J.M. Barthelemy. Two point exponential approximation method for structural optimization. Struct. Optim., 2:117-124, 1990.
5. L. Wang and R.V. Grandhi. Efficient safety index calculations for structural reliability analysis. Comp. Struct., 52:103-111, 1994.
6. L. Wang and R.V. Grandhi. Improved two-point function approximation for design optimization. AIAA J., 33:1720-1727, 1995.
7. S. Xu and R.V. Grandhi. Effective two-point function approximation for design optimization. AIAA J., 36:2269-2275, 1998.
8. A.A. Groenwold, L.F.P. Etman, J.A. Snyman, and J.E. Rooda. Incomplete series expansion for function approximation. In Proc. Sixth World Congress on Structural and Multidisciplinary Optimization, Rio de Janeiro, Brazil, May 2005.
9. A.A. Groenwold, L.F.P. Etman, J.A. Snyman, and J.E. Rooda, Incomplete series expansion for function approximation. Struct. Multidisc. Opt., 2006. Submitted.
10. R.T. Haftka and C.P. Shore. Approximation method for combined thermal/structural design. NASA TP-1428, 1979.
11. A.R. Conn, N.I.M. Gould, and P.L. Toint. Trust-region methods. MPS/SIAM Series on Optimization. SIAM, Philadelphia, 2000.
12. N.M. Alexandrov, J.E. Dennis, R.M. Lewis, and V. Torczon, A trust region framework for managing the use of approximation models in optimization, Struct. Optim., 15:16-23, 1998.
13. J. Nocedal and S. Wright. Numerical Optimization. Springer, Berlin, 1999.
14. G.N. Vanderplaats. Numerical optimization techniques for engineering design. Vanderplaats R&D, Inc., Collorado Springs, 2001.
15. C. Fleury. Structural weight optimization by dual methods of convex programming. Int. J. Numer. Meth. Eng., 14:1761-1783, 1979.
16. J.E. Falk. Lagrange multipliers and nonlinear programming. J. Math. Anal., 19:141-159, 1967.
17. C. Fleury and B. Fraeijs du Veubeke. Structural optimization, In Lecture Notes in Computer Sciences, volume 27, pages 314-326, Berlin, 1975, Springer-Verlag.
18. P. Wolfe, A duality theorem for nonlinear programming. Q. Appl. Math., 19:239-244, 1963.
19. C. Zhu, R.H. Byrd, P. Lu, and J. Nocedal. L-BFGS-B: FORTRAN subroutines for large scale bound constrained optimization, Technical Report NAM-11, Northwestern University, EECS Department, 1994.
20. R.H. Byrd, P. Lu, J. Nocedal, and C. Zhu. A limited memory algorithm for bound constrained optimization, SIAM J. Scient. Comput., 16:1190-1208, 1995.
21. L. Schmit and C. Fleury. Discrete-continuous variable structural synthesis using dual methods. AIAA Journal, 18:1515-1524, 1980.
22. A.A. Groenwold, L.F.P, Etman, and J.E. Rooda. Sequential approximate optimization in an NLP filter framework, In Proc. 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Portsmouth, Virginia, U.S.A., September 2006, Accepted, to appear.
23. R. Fletcher and S. Leyffer. Nonlinear programming without a penalty function. Math. Program., 91:239-269, 2002.
24. R. Fletcher, S. Leyffer, and P.L. Toint, On the global convergence of an SLP-filter algorithm. Technical Report 00/15, Department of Mathematics, University of Namur, Namur, Belgium, 1998.
25. R. Fletcher, S. Leyffer, and P.L. Toint. On the global convergence of a filter-SQP algorithm, SIAM J. Optim., 13:44-59, 2002.
26. M.W. Huang and J.S. Arora. Optimal design with discrete variables: Some numerical experiments. Int. J. Num. Meth. Eng., 40:165-188, 1997.
27. M.P. Bendsøe. Optimal shape design as a material distribution problem. Struct. Optim., 1:193-202, 1989.
28. G.I.N. Rozvany and M. Zhou. Applications of COC method in layout optimization. In H. Eschenauer, C. Mattheck, and N. Olhoff, editors, Proc. Engineering Optimization in Design Processes, pages 59-70, Berlin, 1991. Springer-Verlag.
29. A. Sepúlveda and J. Cassis. An efficient algorithm for the optimum design of trusses with discrete variables. Int. J. Num. Meth. Eng., 23:1111-1130, 1986.
30. M. Beckers. Topology optimization using a dual method with discrete variables. Struct. Optim., 11:102-112, 1996.
31. T.A. Poulsen. A simple scheme to prevent checkerboard patterns and one-node connected hinges in topology optimization. Struct. Multidisc. Opt., 24:396-399, 2002.
32. A.A. Groenwold and L.F.P Etman. Optimality criterion methods and sequential approximate optimization in the classical topology layout problem. In Proc. Eighth International Conference on Computational Structures Technology, Las Palmas de Gran Canaria, Spain, September 2006. Accepted, to appear.
33. M.P. Bendsøe and O. Sigmund. Topology optimization: Theory, methods and applications. Springer, Lyngby, Denmark, 2002.
34. R.D. Cook, D.S. Malkus, M.E. Plesha, and R.J. Win. Concepts and applications of finite element analaysis. John Wiley & Sons, New York, 2002.
35. H.T. Loh and P.Y. Papalambros. A sequential linearization approach for solving mixed-discrete nonlinear design optimization problems. J. Mech. Design, Trans. ASME, 113:325-334, 1991.