Optimization methods in structural reliability

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. Keywords. Structural reliability, constrained minimization, SORM approximations, Lagrange multipliers, asymptotic approximations.