Abstract
In this chapter, we present homotopic (or deformation) methods for studying various classes of variational problems; these are abstract variational problems, problems of the classical calculus of variations, higher-dimensional variational problems, and mathematical programming problems. Conceptually, the homotopic method is based on the following observation: if in the process of deformation of a variational problem, an extremal is uniformly isolated with respect to a parameter, then its property to be a point of minimum is a homotopy invariant. This chapter is devoted to the verification of this principle, which has many applications.
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