Sensitivity theory for nonlinear systems. I. Nonlinear functional analysis approach

Technical Report · Sat Aug 01 04:00:00 EDT 1981

OSTI ID:6083791

Cacuci, D G

Concepts of nonlinear functional analysis are employed to investigate the mathematical foundations underlying sensitivity theory. This makes it possible not only to ascertain the limitations inherent in existing analytical approaches to sensitivity analysis, but also to rigorously formulate a considerably more general sensitivity theory for physical problems characterized by systems of nonlinear equations and by nonlinear functionals as responses. Two alternative formalisms, labeled the Forward Sensitivity Formalism and the Adjoint Sensitivity Formalism, are developed in order to evaluate the sensitivity of the response to variations in the system parameters. The Forward Sensitivity Formalism is formulated in normed linear spaces, and the existence of the Gateaux-differentials of the operators appearing in the problem is shown to be both necessary and sufficient for its validity. Although conceptually straightforward and applicable to a considerably wider range of problems than heretofore possible, this formalism is computationally expensive to employ. The alternative Adjoint Sensitivity Formalism is considerably more economical from a computational standpoint, but, as proven here, it can only be formulated under more restrictive conditions. In particular, the requirement that operators acting on the state vector and on the system parameters must admit densely defined Gateaux-derivatives is shown to be of fundamental importance for the validity of this formalism. The present analysis significantly extends the scope of sensitivity theory and provides a basis for still further generalizations.

• Research Organization: Oak Ridge National Lab., TN (USA)
• DOE Contract Number: W-7405-ENG-26
• OSTI ID: 6083791
• Report Number(s): ORNL/TM-7304; ON: DE81030227
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ANALYTICAL SOLUTION
COMPARATIVE EVALUATIONS
NONLINEAR PROBLEMS
SENSITIVITY ANALYSIS