On diagonal QP subproblems for sequential approximate optimization

Sequential approximate optimization (SAO) methods aimed at structural optimization often use reciprocal-like approximations in a dual setting; the method of moving asymptotes (MMA) and CONLIN are important and telling examples. Using a different (if related) approach, we have previously demonstrated that replacement of the reciprocal approximation by its own quadratic or second order Taylor series expansion may result in equally efficient dual SAO algorithms. In this paper, we show that the quadratic treatment is not only to the benefit of dual SAO statements, but may also make (sparse) sequential quadratic programming (SQP) methods viable for the solution of large-scale structural optimization problems. We solve several test problems by means of a series of diagonal Lagrange-Newton or QP subproblems generated from the quadratic treatment of the objective function and constraint function approximations. We conclude that the proposed SAO method using a QP statement is a very promising alternative when the Falk dual methods become expensive, which may for instance happen for problems with both the number of design variables and the number of constraints very high. As expected, dual methods however remain the most efficient for problems with only a few constraints