On the Boundedness of Lagrange Multipliers of the Kuhn–Tucker Theorem Applied to the Problem of Tikhonov Function Minimization

In the proof of the convergence of sequences of approximations derived by the regularized method of linearization, the Kuhn–Tucker theorem with bounded sequences of Lagrange multipliers is applied to sequences of Tikhonov functions. This paper demonstrates that in the case of three existing forms of constrains: (i) functional inequalities strict at some point, (ii) linear functional inequalities, and (iii) a linear operator equality, there exist bounded sequences of Lagrange multipliers of the Kuhn–Thucker theorem applied to the sequences of Tikhonov functions.