It is known that modern accelerators fall under nonlinear aberrations influence. The most of these aberrations have harmful character, and their effect must be maximally decreased. There are a set of approaches and codes to solving this problem. In this paper, we consider an approach for solving this problem using the matrix formalism for Lie algebraic tools. This formalism allows reducing the starting problem to linear algebraic equations for aberration coefficients, which are elements of corresponding matrices. There are discussed results evaluated using suggested approach and nonlinear programming tools. Some examples of corresponding results are given.