Direct treatment of a max-value cost function in parametric optimization

In dealing with a max-value cost function over the parameter interval in optimization of dynamic systems, we propose a treatment of directly handling the original max-value cost function in order to avoid the computational burden of the transformation treatment using an arti cial design variable. In this paper, it is theoretically shown that the transformation treatment results in demanding an additional equality constraint as a part of the Kuhn{Tucker necessary conditions. Also, it is demonstrated that the usability and feasibility conditions on the search direction of the transformation treatment retard the convergence rate. To investigate the numerical performances of both treatments, typical optimization algorithms in ADS are employed to solve a min{max steady-state response optimization. All the algorithms tested reveal that the suggested direct treatment is more e cient and stable than the transformation treatment. Also, better performance of the direct treatment over the transformation treatment is clearly shown by contrasting the convergence paths in the design space of the sample problem. Three min{max transient response optimization problems are also solved by using both treatments, and the comparisons of the results con rm that the performances of the direct treatment are better than those of the transformation treatment