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Volume 4, Issue 2, 1 August 2020, Pages 301-318
Abstract. This work focuses on identifying a distributed parameter in a saddle point problem with application to the elasticity imaging inverse problem. We examine three optimization formulations for the inverse problem, namely, the output least-squares (OLS), the modified output least-squares (MOLS), and the energy output least-squares (EOLS). The OLS functional and the EOLS functional are, in general, nonconvex; however, we show that the MOLS functional is convex. We provide existence results for optimization problems involving the regularized variants of the OLS, the EOLS, and the MOLS functional. We give first-order and second-order adjoint methods in the continuous setting to compute the first-order and the second-order derivative of the OLS/EOLS functionals. The derivative of the MOLS objective does not involve the derivative of the solution map and hence does not require the adjoint approach. We provide numerical experimentation on tissue phantom data.
How to Cite this Article:
O. Babaniyi, B. Jadamba, A. A. Khan, M. Richards, M. Sama, C. Tammer, Three optimization formulations for an inverse problem in saddle point problems with applications to elasticity imaging of locating tumor in incompressible medium, J. Nonlinear Var. Anal. 4 (2020), 301-318.