Development of a multiplier method for dynamic response optimization problems

The multiplier method is studied for optimum design of mechanical and structural systems subjected to dynamic loads. Certain key parameters in the algorithm are identified and extensive numerical experiments are conducted to see their effect on the performance of the method. Several mathematical programming problems, and static and dynamic response structural design problems are used to evaluate the method. Some new numerical procedures are proposed and evaluated to improve performance of the method. As a result of this study, a better understanding of the multiplier method has been achieved, and the effect of various parameters and procedures of the algorithm is better understood.Notation Number of equality constraints - COST Cost function value at the solution point - CPU Total CPU time on DN10000 - f(x) Cost function - g(x) Constraint vector of dimension m×1 - IFAIL Number of failed problems - A parameter used in the algorithm - L-BFGS Unconstrained minimization program that uses limited memory BFGS method - m Total number of constraints - n Number of design variables - v Number of degrees of freedom - NF Average number of function evaluations - NG Average number of gradient evaluations - NIT Average number of unconstrained minimizations - Parameter vector of dimension m×1 used in the definition of augmented Lagrange functional - r Penalty parameter vector of dimension m×1 - TRDDB Unconstrained minimization program that computes trust region step using the double dogleg method - u Lagrange multiplier vector of dimension m×1 - x Design variable vector of dimension n×1 - x _i Lower bound onx _i - x _ui Upper bound onx _i - (x) Augmented Lagrangian - P(x) Penalty function