A discrepancy principle for equations with monotone continuous operators
It provides a theoretical foundation for parameter choice in regularization of monotone operator equations, which is incremental for the field of inverse problems.
The paper formulates a discrepancy principle for solving nonlinear equations with monotone operators under noisy data, proving existence, uniqueness, and convergence of the regularization parameter. The results are established under natural assumptions on the nonlinear operator.
A discrepancy principle for solving nonlinear equations with monotone operators given noisy data is formulated. The existence and uniqueness of the corresponding regularization parameter $a(δ)$ is proved. Convergence of the solution obtained by the discrepancy principle is justified. The results are obtained under natural assumptions on the nonlinear operator.