An implicit sequential quadratic programming method for large scale structural optimization

Abstract

The basic idea of an implicit sequential quadratic programming (SQP) method for constrained problems is to use the approximate Hessian of the Lagrangian without explicitly calculating and storing it. This overcomes one of the major drawbacks of the traditional SQP method where a large matrix needs to be calculated and stored. This concept of an implicit method is explained and an algorithm based on it is presented. Some details of the steps of the method are presented, such as scaling, restart criterion, etc. A computer program is developed to evaluate the performance of the method. The basic method and some of its variations are evaluated using a set of mathematical programming test problems, and a set of structural design test problems-small to large scale. The method performs much better than a method that does not use any approximate Hessian matrix. Its performance is better than the full SQP method for large scale problems; therefore it is a viable option for large scale optimization.