The book contains about 700 problems for finding extrema for the finite-dimensional case, for problems of classical calculus of variations, optimal control and convex programming. Contains elements of functional analysis, differential calculus, and convex analysis. The book provides the theory needed to solve problems, and examples. The basis for solving all problems is a single principle dating back to Lagrange. Some of the tasks are given with solutions. There are a large number of difficult tasks that can be used as term papers and theses.