  In practice, optimization tasks have some structure that allows developing
new algorithms for every problem with faster convergence rates. Using the
structure of optimization tasks, we can propose algorithms with more optimistic
convergence rates for the following optimization problems: functions with
Holder continuous gradients, superposition of functions (min-max problems),
transportation problems, clustering by electorial model. In this work, we
propose the unification of gradient-type methods into one method using a
special concept of inexact model and develop a series of methods that can solve
generalized optimization problem statements and use its structure with the aid
of the proposed concept of inexact model. We constructed the gradient method
for problems with relative smoothness, the primal--dual adaptive gradient and
fast gradient methods, and the stochastic nonadaptive gradient methods that
support an inexact model of a function. Moreover, the concept of inexact model
is supported by different examples of optimization problems.
