Abstract
This paper presents a numerical performance comparison of a modern version of the well-established sequential quadratic programming (SQP) method and the more recent spherical approximation method (SAM). The comparison is based on the application of these algorithms to examples with nonlinear objective and constraint functions, among others: weight minimization problems in structural shape optimization. The comparison shows that both the SQP and SAM-algorithms are able to converge to accurate minimum weight values. However, because of the lack of a guaranteed convergence property of the SAM method, it exhibits an inability to consistently converge to a fine tolerance. This deficiency is manifested by the appearance of small oscillations in the neighbourhood of the solution.
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References
Arora, J.S. 1989a:Introduction to optimum design. New York: McGraw-Hill
Arora, J.S. 1989b: IDESIGN user's manual version 3.5.2.Technical report No. ODL-89.7, Optimal Design Laboratory, College of Engineering, The University of Iowa
Barthold, F.-J. 1993:Theory and computation of the analysis and optimization of isotropic, hyperelastic structures (in German). Ph.D. Dissertation, University of Hannover
Becker, A. 1992:Structural optimization of stability sensitive systems by means of analytical sensitivity analysis (in German). Ph.D. Dissertation, University of Hannover
Belegundu, A.D. 1985: A study of mathematical programming methods for structural optimization. Part I: theory, Part II: numerical results.Int. J. Num. Meth. Eng. 21, 1583–1623
Bletzinger, K.U. 1990:Shape optimization of surface structures (in German). Ph.D. Dissertation, Institut für Baustatik, Univ. of Stuttgart
Canfield, R. 1995: A rank two Hessian matrix update for sequential quadratic approximation.Proc. 36th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf. (held in New Orleans, LA)
De Klerk, E.; Snyman, J.A. 1994: A feasible descent cone method for linearly constrained minimization problems.Comp. & Math. Appl. 28, 33–44
Fadel, G.M.; Riley, M.F.; Barthelemy, J.M. 1990: Two-point exponential approximation method for structural optimization.Struct. Optim. 2, 117–124
Falk, A. 1995: Adaptive methods for shape optimization of shell structures including CAD-FEM-coupling (in German). Ph.D. Dissertation, Institut für Baumechanik u. Numerische Mechanik, University of Hannover
Haftka, R.T.; Gürdal, Z. 1992:Elements of structural optimization. Boston: Kluwer
Haftka, R.T.; Nachlas, J.A.; Watson, L.T.; Rizzo, T.; Desai, R. 1987: Two-point constraint approximation in structural optimization.Comp. Meth. Appl. Mech. Eng. 60, 289–301
Han, S.-P. 1976: Superlinearly convergent variable metric algorithms for general nonlinear programming problems.Math. Prog. 11, 263–282
Han, S.-P. 1977: A globally convergent method for nonlinear programming.J. Optimiz. Theory Appl. 22, 297–309
Hock, W.; Schittkowski, K. 1981: Test examples for nonlinear programming codes.Lecture Notes in Economics and Mathematical Systems 187. Berlin, Heidelberg, New York: Springer
Mahnken, R. 1992:Dual methods for nonlinear optimization problems in structural mechanics (in German). Ph.D. Dissertation, Institut für Baumechanik u. Numerische Mechanik, University of Hannover
Powell, M.J.D. 1978a: A fast algorithm for nonlinearly constrained optimization calculations. In: Watson, G.A. (ed.)Numerical analysis.Lecture Notes in Mathematics 630. Berlin, Heidelberg, New York: Springer
Powell, M.J.D. 1978b: The convergence of variable metric methods for nonlinearly constrained optimization calculations. In Mangasarian, O.L.; Meyer, R.R.; Robinson, S.M. (eds.)Nonlinear programming 3. New York: Academic Press
Prasad, B. 1983: Explicit constraint approximation forms in structural optimization. Part 1: analyses and projections.Comp. Meth. Appl. Mech. Eng. 40, 1–26
Schittkowski, K. 1981: The nonlinear programming method of Wilson, Han and Powell with an augmented Lagrangian type line search function.Numerische Mathematik 38, 83–114
Schittkowski, K. 1983: On the convergence of a sequential quadratic programming method with an augmented Lagrangian line search function.Optimization, Mathematische Operationsforschung und Statistik 14, 197–216
Schittkowski, K. 1985: On the global convergence of nonlinear programming algorithms.J. Mech. Trans. Auto. Des. 107, 454–458
Schittkowski, K. 1987: More test examples for nonlinear programming codes.Lecture Notes in Economics and Mathematical Systems 282. Berlin, Heidelberg, New York: Springer
Schittkowski, K.; Zillober, C.; Zotemantel, R. 1994: Numerical comparison of nonlinear programming algorithms for structural optimization.Struct. Optim. 7, 1–19
Schmit, L.A.; Farshi B. 1974: Some approximation concepts for structural synthesis.AIAA J. 12, 692–699
Schmit, L.A.; Miura, H. 1976: Approximation concepts for efficient structural synthesis.NASA CR-2552
Snyman, J.A.; Stander, N. 1994: A new successive approximation method for optimum structural design.AIAA J. 32, 1310–1315
Snyman, J.A.; Stander, N. 1996: Feasible descent cone methods for inequality constrained optimization problems.Int. J. Num. Meth. Eng. (to appear)
Stander, N.; Snyman, J.A. 1993: A new first order interior feasible direction method for structural optimization.Int. J. Num. Meth. Eng. 36, 4009–4026
Stander, N.; Snyman, J.A.; Coster, J.E. 1995: On the robustness and efficiency of the SAM algorithm for structural optimization.Int. J. Num. Meth. Eng. 38, 119–135
Starnes, J.H.; Haftka, R.T. 1979: Preliminary design of composite wings for buckling stress and displacement constraints.J. Aircraft 16, 564–570
Sunar, M.; Belegundu, A.D. 1991: Trust region methods for structural optimization using exact second order sensitivity.Int. J. Numer. Meth. Eng. 32, 275–293
Thanedar, P.B.; Arora, J.S.; Tseng, C.H.; Lim, O.K.; Park, G.J. 1986: Performance of some SQP algorithms on structural design problems.Int. J. Numer. Meth. Eng. 23, 2187–2203
Tseng, C.H.; Arora, J.S. 1988: On implementation of computational algorithms for optimal design 1: preliminary investigation and 2: extensive numerical investigation.Int. J. Numer. Meth. Eng. 26, 1383–1402
Venkayya, V.B.; Khot, N.S.; Reddy, V.S. 1968: Energy distribution in an optimum structural design.AFFDL-TR-68-156
Wilson, R.B. 1963:A simplical method for concave programming. Ph.D. Dissertation, Harvard University, Cambridge, Mass., USA
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Barthold, F.J., Stander, N. & Stein, E. Performance comparison of SAM and SQP methods for structural shape optimization. Structural Optimization 11, 102–112 (1996). https://doi.org/10.1007/BF01376852
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DOI: https://doi.org/10.1007/BF01376852