The chapter is devoted to important classic methods frequently used. They are able to tackle nonlinear problems (nonlinear objective function and/or nonlinear constraints). The chapter is divided into three parts. The first part introduces the method of Lagrange multipliers and the KKT optimality conditions. The second considers the variational calculus (mostly due to Euler), with several interesting cases, like the problem of Dido, the problem of Mayer, and the problem of Bolza. The third part departs from the Euler method of finite differences and extends to numerical computational methods based on finite elements. The chapter includes several relevant examples and programs in MATLAB.