  In connection with the needs of solving optimization problems, the
development of conditional minimization methods with convenient numerical
implementation continues to attract the attention of mathematicians. In this
monograph we propose methods for solving mathematical programming problems that
belong to the class of cutting methods. The proposed methods are characterized,
in particular, by the fact that they contain the possibility of periodically
updating approximating sets by discarding accumulating cutting planes, which
makes these methods convenient from a practical point of view. The monograph
can be used by specialists in the field of mathematical programming, as well as
by students studying in the specialties "Applied Mathematics", "Applied
Mathematics and Computer Science", etc.
