Application of variable metric methods to structural synthesis

Abstract

Much recent work in numerical optimization has emphasized the use of variable metric methods which use the Lagrangian. The principal concept is to use a variable metric algorithm to create an approximation to the Lagrangian function. This is used in a quadratic programming sub-problem to find a search direction in design space which will drive the design to the satisfaction of the Kuhn—Tucker necessary conditions for optimality. A one-dimensional search is then performed to achieve the design improvements. Experience with this algorithm applied to structural optimization has shown it to be a powerful design tool. The implementation of this general method will be described, including several modifications for its successful application to practical design. The methods has been implemented in the new general-purpose optimization program, ADS. It is concluded that the algorithm is both a powerful tool for structural optimization, and a good general-purpose algorithm for other design applications.