A choice of the regularization parameter in solving convex extremal problems (Q1975091)

The ill-posed problem of the minimization of a convex functional that is not uniformly convex is ill-posed is considered. The author uses a smoothing-functional method for solving this problem, which is based on the generalized residual principles. The aim this work is the construction of a generalized residual principle of a new form, which is based on another data. Such a problem arises from the fact that even for convex minimized functionals, one has to solve the problems of nonconvex minimization when using the above mentioned method. This sometimes presents unsurmountable difficulties in numerically implementing the method.