A New Approach to the Min-Max Dynamic Response Optimization

For the treatment of a max-value cost function in a dynamic response optimization problem, we propose the approach of directly handling the original max-value cost function in order to avoid the computational burden of the previous transformation treatment. In this paper, it is theoretically shown that the previous treatment results in demanding an additional equality condition as a part of the Kuhn-Tucker necessary conditions. Also, it is demonstrated that the usability and feasibility conditions for the search direction of the previous treatment retard convergence rate. To investigate the numerical performance of both treatments, typical optimization algorithms in ADS are employed to solve a typical example problem. All the algorithms tested reveal that the suggested approach is more efficient and stable than the previous approach. Also, the better performing of the proposed approach over the previous approach is clearly shown by contrasting the convergence paths of the typical algorithms in the design space of the sample problem. Min-max dynamic response optimization programs are developed and applied to three typical examples to confirm that the performance of the suggested approach is better than that of the previous one.