A trust-region framework for managing the use of approximation models in optimization
Tóm tắt
Từ khóa
Tài liệu tham khảo
Avriel, M.; Williams, A.C. 1970: Complementary geometric programming.SIAM J. Appl. Math. 19, 125?141
Barthelemy, J.-F.M.; Haftka, R.T. 1993: Approximation concepts for optimum structural design ? a review.Struct. Optim. 5, 129?144
Braibant, V.; Fleury, C. 1985: An approximation-concepts approach to shape optimal design.Comp. Meth. Appl. Mech. & Eng. 53, 119?148
Carter, R.G. 1986:Multi-model algorithms for optimization. Ph.D. Thesis, Rice University, Houston, TX, USA
Carter, R.G. 1991: On the global convergence of trust region algorithms using inexact gradient information.SIAM J. Num. Analysis 28, 251?265
Chang, K.J.; Haftka, R.T.; Giles, G.L.; Kao, P.-J. 1993: Sensitivity-based scaling for approximating structural response.J. Aircraft 30, 283?288
Dennis, Jr., J.E.; Schnabel, R.B. 1983:Numerical methods for unconstrained optimization and nonlinear equations. Englewood Cliffs, N.J.: Prentice Hall
Dennis, J.E.; Torezon, V. 1997: Managing approximation models in optimization. In: Alexandrov, N.; Hussanini, M.Y. (eds.)Multidisciplinary design optimization state of the art, pp. 330?347. Philadelphia: SIAM
Duffin, R.J.; Peterson, E.L.; Zener, C.M. 1967:Geometric programming, New York: John Wiley & Sons
Fleury, C.; Braibant, V. 1986: Structural optimization a new dual method using mixed variables.Int. J. Num. Meth. Eng. 23, 409?428
Friedlander, A.; Martínez, J.M.; Santos, S.A. 1996: A new trust region algorithm for bound constrained minimization.Tech. Report, Dept. Appl. Math., University of Campinas, Brazil
Gay, D.M. 1982: On convergence testing in model/trust-region algorithms for unconstrained optimization.Computing Science Tech. Report No. 104, Bell Laboratories
Gill, P.E.; Murray, W.; Wright, M.H. 1981:Practical optimization. London: Academic Press
Haftka, R.T.; Shore, C.P. 1979: Approximation methods for combined thermal/structural design.Tech. Report 1428, NASA
Hajela, P. 1986: Geometric programming strategles in large-scale structural synthesis.AIAA J. 24, 1173?1178
Heinkenschloss, M. 1994: On the solution of a two ball trust region subproblem.Math. Prog. 64, 249?276
Moré, J.J. 1983: Recent developments in algorithms and software for trust region methods. In: Bachem, A.; Grötschel, M.; Korte, B. (eds.)Mathematical programming. The state of the the art, pp. 258?287. Berlin, Heidelberg, New York: Springer
Morris, A.J. 1972a: Approximation and complementary geometric programming.SIAM J. Appl. Math. 23, 527?531
Morris, A.J. 1972b: Structural optimization by geometric programming.Int. J. Solids & Struct. 8, 847?864
Morris, A.J. 1974: The optimisation of statically indeterminate structures by means of approximate geometric programming. In:Advisory Group for Aerospace Research and Development, Proc. No. 123, 2nd Symp. on Structural Optimization, pp. 6-1-6-15
Powell, M.J.D. 1975: Convergence properties of a class of minimization algorithms. In: Mangasarian, O.L.; Meyer, R.R.; Robinson, S.M. (eds.)Nonlinear programming 2, pp. 1?27. New York: Academic Press
Schmit, L.A., Jr.; Farshi, B. 1974: Some approximation concepts for structural synthesis.AIAA J. 12, 692?699
Schmit, L.A., Jr.; Fleury, C. 1980: Structural synthesis by combining approximation concepts and dual methods.AIAA J. 18, 1252?1260
Schmit, L.A., Jr.; Miura, H. 1976: Approximation concepts for efficient structural synthesis.Tech. Report CR-2552, NASA
Schultz, G.A.; Schnabel, B.; Byrd, R.H. 1985: A family of trust region based algorithms for unconstrained minimization with strong global convergence properties.SIAM J. Num. Analysis 22, 47?67
Sorensen, D.C. 1982: Newton's method with a model trust region modification.SIAM J. Num. Analysis 19, 409?426
Starnes, J.H., Jr.; Haftka, R.T. 1979: Preliminary design of composite wings for buckling, strength, and displacement constraints.J. Aircraft 16, 564?570
Storaasli, O.O.; Sobieszczanski-Sobieski, J. 1974: On the accuracy of Taylor approximation for structure resizing.AIAA J. 12, 231?233
Templeman, A.B.; Winterbottom, S.K. 1974: Structural design applications of geometric programming. In:Advisory Group for Aerospace Research and Development, Proc. No. 123, 2nd Symp. on Structural Optimization, pp. 5-1-5-15
Vanderplaats, G.N. 1984:Numerical optimization techniques for engineering design. McGraw-Hill