Sequential approximate optimization using dual subproblems based on incomplete series expansions

Structural and Multidisciplinary Optimization

Volumn 36, Issue 6, 2008, Pages 547-570

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

^a STELLENBOSCH UNIVERSITY   (South Africa)

^b EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Duality; Incomplete series expansion (ISE); Sequential approximate optimization (SAO); Structural optimization

Indexed keywords

STRUCTURAL DESIGN; STRUCTURAL OPTIMIZATION;

APPROXIMATE OPTIMIZATIONS; COMPUTATIONAL EXPERIMENTS; CONSTRAINT FUNCTIONS; DEGENERATE CASES; DESIGN VARIABLES; DUALITY; HIGHLY EFFICIENT; INCOMPLETE SERIES EXPANSION (ISE); METHOD OF MOVING ASYMPTOTES; MINIMUM COMPLIANCES; MULTIPOINT APPROXIMATIONS; NONLINEAR; SALIENT FEATURES; SEQUENTIAL APPROXIMATE OPTIMIZATION (SAO); SERIES EXPANSIONS; TOPOLOGY OPTIMIZATIONS; WEIGHT MINIMIZATIONS;

OPTIMIZATION;

EID: 54949144664     PISSN: 1615147X     EISSN: 16151488     Source Type: Journal    
DOI: 10.1007/s00158-007-0197-0     Document Type: Article

References (38)

1. NM Alexandrov JE Dennis RM Lewis V Torczon 1998 A trust region framework for managing the use of approximation models in optimization Struct Optim 15 16 23
2. M Beckers 1996 Topology optimization using a dual method with discrete variables Struct Optim 11 102 112
3. M Bendsøe 1989 Optimal shape design as a material distribution problem Struct Optim 1 193 202
4. Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods and applications. Springer, Berlin Heidelberg New York
5. RH Byrd P Lu J Nocedal C Zhu 1995 A limited memory algorithm for bound constrained optimization SIAM J Sci Comput 16 1190 1208
6. Conn AR, Gould NIM, Toint PL (2000) Trust-region methods. MPS/SIAM series on optimization. SIAM, Philadelphia
7. Cook RD, Malkus DS, Plesha ME, Witt RJ (2002) Concepts and applications of finite element analaysis. Wiley, New York
8. Etman LFP, Groenwold AA, Rooda JE (2006) Sequential approximate optimization in an NLP filter framework. Paper no. AIAA-2006-7078. In: Proceedings of the 11th AIAA/ISSMO multidisciplinary analysis and optimization conference, September 2006, Portsmouth
9. GM Fadel MF Riley JM Barthelemy 1990 Two point exponential approximation method for structural optimization Struct Optim 2 117 124
10. JE Falk 1967 Lagrange multipliers and nonlinear programming J Math Anal Appl 19 141 159
11. R Fletcher S Leyffer 2002 Nonlinear programming without a penalty function Math Program 91 239 269
12. Fletcher R, Leyffer S, Toint PL (1998) On the global convergence of an SLP-filter algorithm. Technical Report 00/15. Department of Mathematics, University of Namur, Namur
13. R Fletcher S Leyffer PL Toint 2002 On the global convergence of a filter-SQP algorithm SIAM J Optim 13 44 59
14. C Fleury 1979 Structural weight optimization by dual methods of convex programming Int J Numer Methods Eng 14 1761 1783
15. C Fleury V Braibant 1986 Structural optimization: a new dual method using mixed variables Int J Numer Methods Eng 23 409 428
16. Fleury C, Fraeijs du Veubeke B (1975) Structural optimization. In: Lecture notes in computer sciences, vol. 27. Springer, Berlin Heidelberg New York, pp 314-326
17. Groenwold AA, Etman LFP (2006) Optimality criterion methods and sequential approximate optimization in the classical topology layout problem. Paper no. CST2006/2005/000216. In: Proceedings of the eighth international conference on computational structures technology, September 2006, Las Palmas de Gran Canaria
18. AA Groenwold LFP Etman 2008 On the equivalence of optimality criterion methods and sequential approximate optimization in the classical topology layout problem Int J Numer Methods Eng 73 297 316
19. Groenwold AA, Etman LFP, Snyman JA, Rooda JE (2005) Incomplete series expansion for function approximation. In: Proceedings of the sixth world congress on structural and multidisciplinary optimization, May 2005, Rio de Janeiro
20. AA Groenwold LFP Etman JA Snyman JE Rooda 2007 Incomplete series expansion for function approximation Struct Multidisc Optim 34 21 40
21. Haftka RT, Shore CP (1979) Approximation method for combined thermal/structural design. NASA TP-1428. NASA, Washington, D.C.
22. MW Huang JS Arora 1997 Optimal design with discrete variables: some numerical experiments Int J Numer Methods Eng 40 165 188
23. HT Loh PY Papalambros 1991 A sequential linearization approach for solving mixed-discrete nonlinear design optimization problems J Mech Des 113 325 334
24. Rozvany GIN, Zhou M (1991) Applications of COC method in layout optimization. In: Eschenauer H, Mattheck C, Olhoff N (eds) Proceedings of engineering optimization in design processes. Springer, Berlin Heidelberg New York, pp 59-70
25. L Schmit C Fleury 1980 Discrete-continuous variable structural synthesis using dual methods AIAA J 18 1515 1524
26. A Sepúlveda J Cassis 1986 An efficient algorithm for the optimum design of trusses with discrete variables Int J Numer Methods Eng 23 1111 1130
27. Sigmund O (1994) Design of material structures using topology optimization. PhD thesis, Technical University of Denmark, Department of Solid Mechanics
28. O Sigmund 1997 On the design of compliant mechanisms using topology optimization Mech Struct Mach 25 495 526
29. JH Starnes Jr RT Haftka 1979 Preliminary design of composite wings for buckling, stress and displacement constraints J Aircr 16 564 570
30. K Svanberg 1987 The method of moving asymptotes-a new method for structural optimization Int J Numer Methods Eng 24 359 373
31. Svanberg K (1995) A globally convergent version of MMA without linesearch. In: Rozvany GIN, Olhoff N (eds) Proceedings of the first world congress on structural and multidisciplinary optimization, Goslar, pp 9-16
32. K Svanberg 2002 A class of globally convergent optimization methods based on conservative convex separable approximations SIAM J Optim 12 555 573
33. Vanderplaats GN (2001) Numerical optimization techniques for engineering design. Vanderplaats R&D, Collorado Springs
34. L Wang RV Grandhi 1994 Efficient safety index calculations for structural reliability analysis Comput Struct 52 103 111
35. L Wang RV Grandhi 1995 Improved two-point function approximation for design optimization AIAA J 33 1720 1727
36. P Wolfe 1963 A duality theorem for nonlinear programming Q Appl Math 19 239 244
37. S Xu RV Grandhi 1998 Effective two-point function approximation for design optimization AIAA J 36 2269 2275
38. Zhu C, Byrd RH, Lu P, Nocedal J (1994) L-BFGS-B: FORTRAN subroutines for large scale bound constrained optimization. Technical Report NAM-11, Northwestern University, EECS Department