%AJadamba, B%AKhan, A.%AKahler, R%ASama, M.%D2018%I
%K
%MOSTI ID: 10063853
%PMedium: X
%TElliptic Inverse Problems of Identifying Nonlinear Parameters
%XInverse problems of identifying parameters in partial differential
equations (PDEs) is an important class of problems with many real-world applications.
Inverse problems are commonly studied in optimization setting with
various known approaches having their advantages and disadvantages. Although
a non-convex output least-squares (OLS) objective has often been used, a convex
modified output least-squares (MOLS) attracted quite an attention in recent
years. However, the convexity of the MOLS has only been established for parameters
appearing linearly in the PDEs. The primary objective of this work
is to introduce and analyze a variant of the MOLS for the inverse problem of
identifying parameters that appear nonlinearly in variational problems. Besides
giving an existence result for the inverse problem, we derive the first-order and
second-order derivative formulas for the new functional and use them to identify
the conditions under which the new functional is convex. We give a discretization
scheme for the continuous inverse problem and prove its convergence. We
also obtain discrete formulas for the new MOLS functional and present detailed
numerical examples.
Country unknown/Code not availableOSTI-MSA