Abstract
In this paper a method for constrained minimization of functions is outlined. This method is similar to the method developed by Hasofer/Lind and Rackwitz/Fiessler; but firstly it can be generalized to problems with several constraints and secondly under slight regularity conditions its convergence can be demonstrated.
Further it is shown that the sequential quadratic programming schemes, which produce an approximate Hessian of the Lagrangian, can be used easily for calculating SORM approximations, since the determinant of this Hessian divided by the squared length of the gradient of the limit state function is the inverse of the square of the SORM correction factor.
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References
K. Breitung. Asymptotic approximations for multinormal integrals. Journal of the Engineering Mechanics Division ASCE, 110 (3): 357–366, 1984.
K. Breitung. Asymptotic Approximations for Probability Integrals. Springer, Berlin, 1994. Lecture Notes in Mathematics, Nr. 1592.
K. Breitung and L. Faravelli. Response surface methods and asymptotic approximations. In F. Casciati and J.B. Roberts, editors, Mathematical Models for Structural Reliability, chapter 5, pages 237–298. CRC, Boca Raton, FL, 1996.
F. Casciati and L. Faravelli. Fragility Analysis of Complex Structures. Research Studies Press Ltd., Taunton, UK, 1991.
M. Hohenbichler, S. Gollwitzer, W. Kruse, and R. Rackwitz. New light on first-and second-order reliability methods. Structural Safety, 4: 267–284, 1987.
P.-L. Liu and A. Der Kiureghian Optimization algorithms for structural reliability. Structural Safety, 9 (3): 161–177, 1991.
H. Madsen, S. Krenk, and N.C. Lind. Methods of Structural Safety. Prentice-Hall Inc., Englewood Cliffs, N.J., 1986.
B.N. Pshenichnyj. Algorithms for general mathematical programming problems. Cybernetics,6(5):120–125, 1970. Translation of the journal “Kibernetika”.
B.N. Pshenichnyj. The Linearization Method for Constrained Optimization. Springer, Berlin, 1994.
R. Rackwitz and B. Fiessler. Structural reliability under combined random load sequences. Computers and Structures, 9: 489–494, 1978.
K. Schittkowski. On the convergence of a sequential quadratic programming method with an augmented Lagrangian line search function. Math. Operationsforschung and Statistik, Ser. Operationsforschung, 14: 197–216, 1983.
D. Veneziano, F. Casciati, and L. Faravelli. Method of seismic fragility for complicated systems. In Proc. 2nd Specialist Meeting on Probabilistic Methods in Seismic Risk Assessment for Nuclear Power Plants, pages 67–88, Livermore, 1983.
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Breitung, K., Casciati, F., Faravelli, L. (1998). Optimization Methods in Structural Reliability. In: Marti, K., Kall, P. (eds) Stochastic Programming Methods and Technical Applications. Lecture Notes in Economics and Mathematical Systems, vol 458. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45767-8_22
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DOI: https://doi.org/10.1007/978-3-642-45767-8_22
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