Some features of the nonlinear optimization problem

The subject of this article is some features of the nonlinear optimization problem. An algorithm and examples of solving nonlinear optimization problems using the generalized Lagrange function, necessary and sufficient conditions of the 1st and 2nd order extremum are presented. Numerous forms of writing and Lagrange functions and constraints are considered, and the simplest, most understandable components of a nonlinear optimization problem are formulated. Conclusions are drawn about the cases of application of classical and generalized Lagrange functions.