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

摘要

In the proot of the convergence ot sequences oi 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.