Principles of Optimal Design: Modeling and Computation by Panos Y. Papalambros & Douglass J. Wilde

Author:Panos Y. Papalambros & Douglass J. Wilde [Papalambros, Panos Y.]
Language: eng
Format: epub
Publisher: Cambridge University Press
Published: 2017-01-31T08:00:00+00:00

Sensitivity Coefficients

When small changes in the values of the parameters (or constants) are considered, we have a problem of sensitivity analysis. In this case, small changes in the values of the parameters produce a perturbation in the values of the constraint functions . In the standard form of nonlinear programming, such perturbations correspond to small deviations from the zero value of the constraints. Thus, sensitivity analysis studies the influence of perturbations about the point , on the values and . Active inequalities may be included in the same way as equalities.

Let be a feasible optimum and a vector of perturbations about . Corresponding to , there will be perturbations about . Using the partition of state and decision variables , we have

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