Operation Research 21: Nonlinear Programming Problem

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.
A feasible solution is a local optimum if no other feasible solutions with a better objective function value are found in the immediate neighborhood.
A point is a local maximum if no other feasible solutions with a larger objective function value are in the immediate neighborhood.
Nonlinear optimization problems can have multiple local optimal solutions.
A feasible solution is a global optimum if no other feasible points with a better objective function value are found in the feasible region.
In the case of a maximization problem, the global optimum corresponds to a global maximum. For a minimization problem, a point is a global minimum if no other feasible points with a strictly smaller objective function value are in the feasible region.
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.
Thus, we will use the principles of differentiations to identify the maxima and the minima.