Observations on Extrapolations Using Parameter Sensitivity Derivatives

Abstract

Abstract Parameter sensitivity analysis refers to the estimation of changes in the modeling functions and current design point due to small changes in the fixed parameters of the formulation. Several methods exist for estimating these derivatives without performing a reoptimization at the desired values of the parameters. These methods generally assume that the current active set of constraints do not change. When this is not the case, then significant errors in any extrapolations based on the derivatives can occur near the values of the parameters that produce the change in the active set. This paper will discuss how extrapolations based on sensitivity derivatives are effected by changes in the active set. We identify four different cases of active set changes : a constraint leaving the active set, a constraint entering the active set, an active set change that results in a linear dependency in the constraint gradients, and a change that eliminates the feasible region. We will discuss each of these cases separately, and show that the sources of error in the extrapolations are due primarily to discontinuties in the sensitivity derivatives. We present some examples showing these discontinuities, and describe an algorithm to deal with the first three cases of active set changes.