Min-max dynamic response optimization of mechanical systems using approximate augmented Lagrangian

A globally convergent and e¦cient algorithm for minÐmax dynamic response optimization using the ALM method is presented. This algorithm employs an approximate augmented Lagrangian for line searches, and an exact augmented Lagrangian for Þnding search directions. This approximate augmented Lagrangian is composed of the linearized cost and constraint functions projected on the search direction. It is noted that an approximate penalty term has the same approximate Hessian as that of the GaussÐNewton method. This makes the approximate augmented Lagrangian to have almost second-order accuracy near the optimum. In the unconstrained optimization process of the proposed method, some modiÞcations are also suggested to remove the possible distortion of optimization trajectory when the side constraints on design variables are separately handled. Also, the e¦ciencies of two treatments for handling a max-value cost function are discussed in the context of the proposed method. The numerical performance of the proposed method is investigated by solving three minÐmax dynamic response optimization problems and comparing the results with those in the literature. This comparison shows that the suggested algorithm is more e¦cient than those in the literature. Especially, it is found that the direct treatment for a max-value cost function is more e¦cient than the transformation treatment for all the design cases