HLRF-BFGS-Based Algorithm for Inverse Reliability Analysis

Algorithm 2

BFGS-based hybrid algorithm.

Select target reliability index .

Select the starting point values for and as and .

; is the iteration counter.

.

is fixed as the identity matrix for the first iteration ().

REPEAT (while the convergence criterion is not satisfied)

    The same as step (1) in the intermediate algorithm.

   The same as step (2) in the intermediate algorithm.

   The same as step (3) in the intermediate algorithm.

   The same as step (4) in the intermediate algorithm.

   The same as step (5) in the intermediate algorithm.

   The same as step (6) in the intermediate algorithm.

   If OR determinant of inverse of BFGS matrix diverges away from

     ;

     fix the inverse of Hessian as identity matrix .

    else

    update inverse of Hessian as using the BFGS update formula shown in Eq. (20).

    where is the inverse of BFGS matrix in the th iteration and k is the variable to

    keep track of the determinant of . k has an initial value of 0.

    END

    .

END