Dynamic response optimization using an active set RQP algorithm

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Abstract
A recently developed recursive quadratic programming (RQP) algorithm is applied to dynamic response design problems. The algorithm incorporates updated Hessians of the Lagrange function and uses an active set strategy in which only a subset of the constraints is included in the direction finding QP subproblem. Hessian updating with dynamic response constraints presents some difficulties. The primary difficulty is that the total number of constraints and the location of time points where they have to be imposed can change from iteration to iteration. This can cause inconsistencies in Hessian updating if proper numerical procedures are not used. A numerical procedure to handle the situation is developed, implemented and evaluated. Automatic restarting procedures are necessary for proper convergence of the algorithm. The new algorithm is robust as well as more efficient than the purely linear algorithm. The active set strategy plays an important role for application to dynamic response problems. The RQP algorithms that do not use such a strategy are not applicable to this class of problems.

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