A discrepancy principle for equations with monotone continuous operators

TL;DR

This paper introduces a discrepancy principle for solving nonlinear equations with monotone operators using noisy data, establishing existence, uniqueness, and convergence of the regularization parameter and solution under natural assumptions.

Contribution

It formulates a new discrepancy principle for monotone operators, proving existence, uniqueness, and convergence of the regularization parameter and solution.

Findings

Existence and uniqueness of the regularization parameter $a(elta)$ are proved.

Convergence of the regularized solution is justified.

Results hold under natural assumptions on the nonlinear operator.

Abstract

A discrepancy principle for solving nonlinear equations with monotone operators given noisy data is formulated. The existence and uniqueness of the corresponding regularization parameter $a(\delta)$ is proved. Convergence of the solution obtained by the discrepancy principle is justified. The results are obtained under natural assumptions on the nonlinear operator.