Maximization or minimization of a function f(**x**)
subject to conditions g_{i}(x)
0, i = 1, 2, …, m (which is often refer to as optimization), is frequently
studied through the Lagrange-multiplier method. Lagrangian function (often
"Lagrangian") is composed from both objective function and restricting
conditions into one function

f(x) .

The sign "+" holds when g_{i}(x)
0, and sign "-" when g_{i}(x)
0. New variables u_{i} are called Lagrangian multipliers.

Lagrangian function enables one obtain an optimization problem without constraints, and the optimum is find by equating the first partial derivatives to zero and using ideas of traditional mathematical analysis. Thus Lagrangian function associated to nonlinear programming problem utilises the problem of finding the solution.