  The optimization algorithms for solving multi-parameter inverse problem for
the mathematical model of parabolic equations arising in social networks,
epidemiology and economy are investigated. The data fitting is formulated as
optimization of least squares misfit function. Firstly, the tensor train
decomposition approach is presented as global convergence algorithm. The idea
of proposed method is to extract the tensor structure of the optimized
functional and use it for optimization. Then the inverse problem solution is
reached by implementation of the local gradient approach. The evident formula
for the gradient of the misfit function is obtained. The inverse problem for
the diffusive logistic mathematical model described online social networks is
solved by combination of tensor train optimization and local gradient methods.
The numerical results are presented and discussed.
