Smooth-polylines vs. polynomials in balanced identification technology: solving inverse problems of thermal conductivity

Various parameters' identification problems of one-dimensional nonlinear heat equation are considered. Their numerical study was carried out on the basis of balanced identification technology, which provides a compromise between the simplicity of the model (the curvature of the functions) and the proximity to experimental data. The problem of identifying functions whose arguments are model variables is considered. When approximating such a function, we had to use a polynomial function – the use of polylines (polygonal lines) in this case (superposition of functions) leads to nonsmooth mathematical programming problems (with discontinuous derivatives) with the solution not supported by standard solvers. An investigation of the use of special smooth approximations of polygonal curves (smooth-polylines) is presented.