Lavrentiev Regularization methods for Ill-posed equations

This chapter considers the problem of approximately solving the nonlinear ill-posed operator equation by expanding the applicability of the Lavrentiev regularization methods. It presents basic assumptions and some preliminary results of the Lavrentiev regularization methods. The chapter provides main order optimal result using the apriori parameter choice and the posteriori parameter choice. It also includes numerical examples for solving the nonlinear ill-posed operator equation.