A study on the treatment of a max-value cost function in parametric optimization

매개변수 종속 최적화에서 최대치형 목적함수 처리에 관한 연구

  • Kim, Min-Soo (Dept. of Mechanical Design, Graduate School of Hanyang University) ;
  • Choi, Dong-Hoon (Dept. of Mechanical Design, Hanyang University)
  • 김민수 (한양대학교 대학원 기계설계학과) ;
  • 최동훈 (한양대학교 기계설계학과)
  • Published : 1997.10.01


This study explores the treatment of the max-value cost function over a parameter interval in parametric optimization. To avoid the computational burden of the transformation treatment using an artificial variable, a direct treatment of the original max-value cost function is proposed. It is theoretically shown that the transformation treatment results in demanding an additional equality constraint of dual variables 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 convergence rate. To investigate numerical performances of both treatments, typical optimization algorithms in ADS are employed to solve a min-max steady-state response optimization. All the algorithm tested reveal that the suggested direct treatment is more efficient and stable than the transformation treatment. Also, the better performing of the direct treatment over the transformation treatment is clearly shown by constrasting the convergence paths in the design space of the sample problem. Six min-max transient response optimization problems are also solved by using both treatments, and the comparisons of the results confirm that the performances of the direct treatment is better than those of the tranformation treatment.


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