Application of a Reduced Quadratic Programming Technique to Optimal Structural Design

Abstract : A recently developed optimization technique of great practical potential will be presented. The technique is based on two developments. First, it utilizes a successive Quadratic Programming algorithm originally presented by Han and implemented by Powell for solving nonlinear constrained optimization problems. A Quasi-Newton method in used to approximate the Hessian matrix, resulting in near-quadratic convergence to at least a local optimum. Second, the procedure uses the work of Berna et al., who developed a decomposition procedure for the Han-Powell algorithm. The procedure partitions the original design variables into independent and dependent variables, eliminates the dependent variables, and thus yields a much reduced Quadratic Programming problem to be solved at each iteration. Results obtained with the technique for a number of standard test problems, which include the 10 bar truss, the 25 bar truss and the 72 bar truss problems, are in agreement with previous results and show a general reduction of the number of cycles to convergence, especially for the optimal structural design problems with stress constraints only. (Author)