An analysis of collaborative optimization methods

8th Symposium on Multidisciplinary Analysis and Optimization

Volumn , Issue , 2000, Pages

  Demiguel, Angel Victor ^a   Murray, Walter ^a  

^a Stanford University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BENDER'S DECOMPOSITION; COLLABORATIVE OPTIMIZATION; DECOMPOSITION ALGORITHM; LINEAR PROBLEMS; OPTIMIZATION PROBLEMS; SINGLE- MACHINES; TECHNICAL CHALLENGES; WEAK CONNECTIVITIES;

SCHEDULING ALGORITHMS;

EID: 85045481299     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2514/6.2000-4720     Document Type: Conference Paper

References (37)

1. N.M. Alexandrov and M.Y. Hussaini, editors. Multidisciplinary Optimization: State of the Art, Philadelphia, 1997. SIAM.
2. N.M. Alexandrov and S. Kodiyalam. Initial results of an MDO method evaluation study. In Seventh AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, 1998. AIAA Paper 98-4884.
3. N.M. Alexandrov and R.M. Lewis. Comparative properties of collaborative optimization and other approaches to MDO. In Proc., First ASMO UK/ISSMO conference on Engineering Design Optimization. MCB Press, jul 1999.
4. N.M. Alexandrov and R.M. Lewis. Analytical and computational aspects of collaborative optimization. Technical Report TM-2000-210104, NASA, 2000.
5. J.P. Aubin and H. Frankowska. Set-Valued Analysis. Birkhauser, 1990.
6. R.J. Balling and J. Sobieszczanski-Sobieski. An algorithm for solving the system-level problem in multilevel optimization. Structural Optimization, 9:168-177, 1995.
7. R.J. Balling and J. Sobieszczanski-Sobieski. Optimization of coupled systems: a critical overview of approaches. AIAA Journal, 34(1):6-17, 1996.
8. R.J. Balling and C.A. Wilkinson. Execution of multidisciplinary design optimization approaches on common test problems. AIAA Journal, 35:178-186, 1997.
9. A. Barclay, P.E. Gill, and J.B. Rosen. SQP methods and their application to numerical optimal control. Technical Report Report NA 97-3, Department of Mathematics, University of California, San Diego, 1998.
10. J.F. Bard. Practical bilevel optimization: Algorithms and applications. Kluwer academic publishers, 1998.
11. J.F. Benders. Partitioning procedures for solving mixed variables programming problems. Numerische Mathematik, 4:238-252, 1962.
12. E.G. Boman. Infeasibility and negative curvature in optimization. PhD thesis, Stanford, 1999.
13. R.D. Braun. Collaborative Optimization: An architecture for large-scale distributed design. PhD thesis, Stanford, 1996.
14. R. Courant. Variational methods for the solution of problems with equilibrium and vibration. Bull. Amer. Math. Soc, 49:1-23, 1943.
15. E.J. Crammer, J.E. Dennis, P.D. Frank, R.M. Lewis, and G.R. Shubin. Problem formulation for multidisciplinary optimization. SIAM J. Optimization, 4(4):754-776, November 1994.
16. G.B. Dantzig and P. Wolfe. Decomposition principle for linear programs. Operations Research, 8(1):101-111, 1960.
17. A.V. DeMiguel. Collaborative Optimization: A decomposition algorithm for dual-angular nonlinear problems. PhD thesis, Stanford, In preparation.
18. S. Dempe. A bundle algorithm applied to bilevel programming problems with non-unique lower level solutions. Computational Optimization and Applications, 15 (2): 145-166, 2000.
19. J.E. Falk and J. Liu. On bilevel programming, part I: general nonlinear cases. Mathematical Programming, 70:47-72, 1995.
20. A.V. Fiacco and G.P. McCormick. Nonlinear programming: sequential unconstrained minimization techniques. John Wiley and Sons, 1968.
21. O.E. Flippo and A.H.G. Rinnooy Kan. Decomposition in general mathematical programming. Mathematical Programming, 60:361-382, 1993.
22. A.M. Geoffrion. Generalized Benders decomposition. Journal of Optimization Theory and Applications, 10(4), 1972.
23. P.E. Gill, W. Murray, and M.A. Saunders. SNOPT: An SQP algorithm for large-scale constrained optimization. Technical report, Dept. of Mathematics, University of California, 1997. To appear in SIAM J. Optimization.
24. RE. Gill, W. Murray, and M.H. Wright. Practical Optimization. Academic Press, 1981.
25. R. T. Haftka and J. Sobieszczanski-Sobieski. Multidisciplinary aerospace design optimization: Survey of recent developments. Structural Optimization, 14:1-23, 1997.
26. J. Hiriart-Urruty and C. Lemarechal. Convex Analysis and minimization algorithms. Springer-Verlag, 1993.
27. G. Infanger. Planning under uncertainty: solving large-scale stochastic linear programs. Boyd and Eraser, 1994.
28. J.E. Kelley. The cutting plane method for solving convex programs. J. Soc. Indust. Appl. Math., 8:703-712, 1960.
29. I.M. Kroo. Decomposition and collaborative optimization for large-scale aerospace design programs. In N.M. Alexandrov and M.Y. Hussaini, editors, Multidisciplinary Design Optimization: State of the art, 1997.
30. V.M. Manning. Large-scale design of supersonic aircraft via collaborative optimization. PhD thesis, Stanford, 1999.
31. W. Murray. Analytical expressions for the eigenvalues and eigenvectors of the hessian matrices of barrier and penalty functions. Journal of Optimization Theory and Applications, 7:189-196, 1971.
32. W. Murray and F.J. Prieto. A sequential quadratic programming algorithm using an incomplete solution of the subproblem. SIAM J. Optimization, 1995.
33. J. Nocedal and S.J. Wright. Numerical Optimization. Springer-Verlag, 1999.
34. H. Schramm and J. Zowe. A version of the bundle idea for minimizing a nonsmooth function: conceptual idea, convergence analysis, numerical results. SIAM J. Optimization, 2:121-152, 1992.
35. K. Shimizu, Y. Ishizuka, and J.F. Bard. Nondif-ferentiable and two-level mathematical programming. Kluwer academic publishers, 1997.
36. I.P. Sobiesky. Multidisciplinary design using collaborative optimization. PhD thesis, Stanford, 1998.
37. M.H. Wright. Ill-conditioning and computational error in interior methods for nonlinear programming. SIAM J. Optimization, 9:84-111, 1999.