Regularization method with two parameters for nonlinear ill-posed problems (Q2481279)

The paper is concerned with solution methods for ill-posed operator inclusions \(y_0 \in F(x)\) \((x \in D(F))\) in a Banach space \(X\). The authors establish the convergence of multivalued Tikhonov's regularization method \[ \inf_{x \in D(F)} \inf_{y \in F(x)} \{ \| y-y_0\|^2+ \alpha \| Lx-Lx^* \|^2+ \beta \| x\|^2 \}, \] where \(L\) is a closed linear operator and \(x^* \in X\), \(\alpha, \beta>0\) are parameters.