Abstract
This article considers the numerical solution of the direct and inverse problems of the gas lift process in oil production, described by a system of hyperbolic equations. The inverse problem is reduced to an optimal control problem, where the control is the initial velocity of the gas. To minimize the quadratic objective functional, the gradient method is used, in which the gradient is determined using the conjugate equation method. The latter involves constructing a conjugate problem based on the Lagrange identity and the duality principle. Solving the conjugate problem allows us to obtain an analytical expression for the gradient of the functional and effectively implements the Landweber iterative method. A numerical experiment was carried out that confirmed the effectiveness of the proposed method in optimizing the parameters of the gas lift process.