High order sensitivity analysis of complex, coupled systems

The Sobieszczanski-Sobieski (1988) algorithm is extended to include second- and higher-order derivatives while retaining the obviation of finite-differencing of the system analysis. This is accomplished by means of a recursive application of the same implicit function theorem as in the original algorithm. In optimization, the computational cost of the higher-order derivatives is relative to the aggregate cost of analysis together with a repetition of the first-order sensitivity analysis as often as is required to produce the equivalent information by successive linearizations within move limits.