A Recursive Quadratic Programming Based Method for Estimating Parameter Sensitivity Derivatives

Abstract

Parameter sensitivity analysis is defined as the estimation of changes in the modeling functions and design point due to small changes in the fixed parameters of the formulation. There are currently several methods for estimating parameter sensitivities which either require second order information, or do not return reliable estimates for the derivatives. This paper presents a method based on the use of the recursive quadratic programming method in conjunction with differencing formulas to estimate parameter sensitivity derivatives without the need to calculate second order information. In addition, a modified variable metric method for estimating the Hessian of the Lagrangian function is presented that is used to increase the accuracy of the sensitivity derivatives. Testing is performed on a set of problems with Hessians obtained analytically, and on a set of engineering related problems whose derivatives must be estimated numerically. The results indicate that the method provides good estimates of the parameter sensitivity derivatives on both test sets.