On the equivalent static loads approach for dynamic response structural optimization

The equivalent static loads algorithm is an increasingly popular approach to solve dynamic response structural optimization problems. The algorithm is based on solving a sequence of related static response structural optimization problems with the same objective and constraint functions as the original problem. The optimization theoretical foundation of the algorithm is mainly developed in Park and Kang (J Optim Theory Appl 118(1):191–200, 2003). In that article it is shown, for a certain class of problems, that if the equivalent static loads algorithm terminates then the KKT conditions of the original problem and the final sub-problem are identical. The proof of this important theoretical result is unfortunately both incomplete and incorrect and the result is generally not valid. The missing parts of the proof are herein identified and corrected and the critical mistake in the proof is located and explained. We suggest a modified method in the same spirit for which the requested result is proved.