Optimal redesign in the presence of system constraint perturbations

Abstract

Two methods for estimating optimal solutions to nonlinear-programming problems (NLP), with perturbed constraints are developed. The first is a second order Classical Perturbation Analysis. The second is a labelling technique which involves the assumption of low constraint curvature near the optimal solution. These estimation procedures require the Hessians of the cost and constraint functions, and so, procedures for estimating the Hessian of a function are also discussed. Both estimation procedures are compared to an exact solution for a simple problem. For this simple example the labelling technique provided a better estimate than the perturbation technique. What might be termed conventional methods for solving complex NLP problems with perturbed constraints include using the initial guess from the unperturbed problem as the initial guess for the perturbed problem, and using the final solution to the unperturbed problem as the initial guess for the perturbed problem. The estimated solutions can also be used as an initial guess in an iterative NLP problem solution. The results using these estimation procedures are compared to the conventional methods. The labelling technique, being limited to small curvature, was not capable of estimating a solution to the more complex example. Results for this complex example show that the Classical Perturbation Method provides a factor of seven improvement in computational effort over the use of the unperturbed initial guess, and a factor of four improvement over the use of the unperturbed optimal solution as an initial guess.