Inverse problems have been studied in great detail and optimization methods using objective functionals such as output least-squares (OLS) and modified output least-squares (MOLS) are well understood. However, the existing literature has only dealt with identifying parameters that appear linearly in systems of partial differential equations. We investigate the changes that occur in the identification process if the parameter appears nonlinearly. We extend the OLS and MOLS functionals to this nonlinear case and give first and second derivative formulas. We further show that the typical convexity of the MOLS functional can not be guaranteed when identifying nonlinear parameters. To numerically verify our findings we employ a C++ based computational framework. Discretization is done via the finite element method, and details are given for the new results of the functionals and their derivatives. Since we consider nonlinear parameters, gradient methods such as adjoint stiffness are not applicable to the OLS functional and we instead show computation methods using the adjoint approach.

Library of Congress Subject Headings

Differential equations, Partial--Numerical methods; Differential equations, Nonlinear; Inverse problems (Differential equations); Mathematical optimization

Publication Date


Document Type


Student Type


Degree Name

Applied and Computational Mathematics (MS)

Department, Program, or Center

School of Mathematical Sciences (COS)


Baasansuren Jadamba

Advisor/Committee Member

Akhtar A. Khan

Advisor/Committee Member

Patricia Clark


Physical copy available from RIT's Wallace Library at QA377 .K34 2016


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