Quantitative Analysis for Management, 13/e

10.4 Nonlinear Programming

Linear, integer, and goal programming all assume that a problem’s objective function and constraints are linear. That means that they contain no nonlinear terms such as $X_1{3}^{}, 1/X_2,\text{ log }{X}_3$, or $5X_1{X}_2$. Yet in many mathematical programming problems, the objective function and/or one or more of the constraints are nonlinear.

Unlike with linear programming methods, computational procedures for solving many nonlinear programming (NLP) problems do not always yield an optimal solution. In many NLP problems, a particular solution may be better than any other point nearby, but it may not be the overall best point. This is called a local optimum, and the overall best solution is called the global optimum. Thus, for a particular ...