Coefficient identification problems for non-stationary production-loss models are considered. Such models are widely used in chemical, environmental, economic, and biological process studies. The objective of the work is to numerically compare standard derivative-free and gradient-based optimization algorithms accuracy to that of the algorithm consisting of solving the quasi-linear matrix equation with the sensitivity operator. The matrix equation is solved by means of the Newton-Kantorovich-type algorithm with the truncated SVD regularized matrix inversion. Both gradient and sensitivity operator-based algorithms use adjoint problems. The algorithms are compared on the inverse modeling scenario for the antioxidant system of a plant cell. In the scenario, the parameters of the model with rational production-loss operators have to be identified by the state function measurements with the regular time steps. In the numerical experiments, the adjoint problem-based algorithms showed almost the same accuracy, while derivative-free algorithms were less accurate. The largest errors of the latter were obtained on the model coefficients that were not identified by the adjoint problem-based algorithms.