When is DiESL=ESL for linear dynamic response structural optimization?

The Difference-based Equivalent Static Loads (DiESL) algorithm modifies the original ESL algorithm for nonlinear dynamic response structural optimization. The modifications in DiESL reportedly result in better approximations in the static response sub-problem and thus improved convergence properties of the algorithm. We study DiESL when applied to the special case of linear dynamic response structural optimization problems. Under certain assumptions, the two algorithms become identical in the sense that the static response sub-problems are equivalent.