Operation Research 22: Nonlinear Programming Problem Optimization using Lagrange Multiplier.

Nonlinear Programming Problem: A nonlinear optimization problem is any optimization problem in which at least one term in the objective function or a constraint is nonlinear.
Many business processes behave in a nonlinear manner.
Nonlinear programming has the same format as a linear programming model, but the objective function or constraints, or both, are nonlinear functions.
Most mathematical techniques for solving nonlinear programming problems are very complex.
The method of Lagrange multipliers is a general mathematical technique that can be used for solving constrained optimization problems consisting of nonlinear objective function and one or more linear or nonlinear constraint equations.
In the method of Lagrange multipliers, constraints as multiples of multipliers, ʎ, are subtracted from the objective function, which is then differentiated with respect to each variable and solved.