HLRF-BFGS optimization algorithm for structural reliability

In this work we briefly discuss some concepts of structural reliability as well as the optimization algorithm that is commonly used in this context, called HLRF. We show that the HLRF algorithm is a particular case of the SQP method, in which the Hessian of the Lagrangian is approximated by an identity matrix. Motivated by this fact, we propose the HLRF-BFGS algorithm that considers the BFGS update formula to approximate the Hessian. The algorithm proposed herein is as simple as the HLRF algorithm, since it requires just one function and gradient evaluation at each iteration and the new iterate is given by a recursive formula. Comparative numerical experiments on a set of problems selected from the literature are presented to illustrate the performance of the algorithm and the results indicate that the HLRF-BFGS algorithm has the advantage of being more robust and efficient with respect to the function and gradient evaluation, than HLRF.