抄録
A new formulation is proposed to determine the minimal objective function under inequality constraint conditions. Taylor series expansion of the objective function with respect to design variables is employed for the approximation up to the quadratic terms by use of the Hessian matrix, while linear approximation is employed for the inequality constraint conditions. The objective function is standardized on the basis of the eigenvalue analysis of the Hessian matrix so as to form the hypersphere. The center of the hypersphere is used directly for the minimization of the objective function in the case that the center lies inside the feasible domain of the design variables. In the case that the center is outside the feasible domain, the minimal value of the objective function is searched for as the hypersphere tangent to the hyperplanes which represent the boundary of the feasible domain. The numerical examples in problem of beam vibration show that the proposed method is straightforward and efficient in searching for minimal objective function.
