A nonmonotone line search technique for Newton's method
SIAM Journal on Numerical Analysis
Shapes and geometries: analysis, differential calculus, and optimization
Shapes and geometries: analysis, differential calculus, and optimization
On the Convergence of Pattern Search Algorithms
SIAM Journal on Optimization
Nonmonotone Spectral Projected Gradient Methods on Convex Sets
SIAM Journal on Optimization
Pattern Search Methods for Linearly Constrained Minimization
SIAM Journal on Optimization
Engineering Applications of Artificial Intelligence
Tumor location and parameter estimation by thermography
Mathematical and Computer Modelling: An International Journal
Realistic rendering of organ for surgery simulator
Computers & Mathematics with Applications
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In non-invasive thermal diagnostics, accurate correlations between the thermal image at skin surface and interior human physiology are desired. In this work, an estimation methodology to determine unknown geometrical parameters of an embedded tumor is proposed. We define a functional that represents the mismatch between a measured experimental temperature profile, which may be obtained by infrared thermography on the skin surface, and the solution of an appropriate boundary problem. This functional is related to the geometrical parameters through the solution of the boundary problem, in such a way that finding the minimum of this functional form also means finding the unknown geometrical parameters of the embedded tumor. Sensitivity analysis techniques coupled with the adjoint method were considered to compute the shape derivative of the functional. Then, a nonmonotone spectral projected gradient method was implemented to solve the optimization problem of finding the optimal geometric parameters.