On stability of extremal problems in Banach space

Problems of stability and a method of regularization of extremal problems in Banach spaces are considered. Criteria for the convergence and stability of the method considered are given in terms of the geometry of the unit balls of the Banach spaces for a wide class of functionals and restrictions. A means of reducing the problems to a finite-dimensional analog is indicated. The connection with known conditions for the convergence of minimizing sequences in extremal problems is discussed.
Bibliography: 19 titles.