An optimization approach to solving a discrete inverse problem for a one-dimensional hyperbolic equation

In this paper, an optimization approach to solving a discrete problem of determining the coefficient of a one-dimensional hyperbolic equation in integral formulation is studied. The properties of the solutions to the inverse and direct discrete problems are investigated. Estimates both for the cost function and its gradient are obtained. Also, the convergence of the steepest descent method minimizing the misfit functional is proved.