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Operations Research Models and Methods
Computation Section
Subunit Nonlinear Programming
 For nonlinear programming models some terms of the objective function or constraints involve nonlinear functions of the decision variables. Although the statement of the nonlinear model is similar to the linear programming model, the process of solving such problems is significantly more complicated.

The figure shows a linearly constrained region and contours of a nonlinear objective function. We solve this example later in this section.

  The Excel Solver finds solutions for nonlinear programming models, but the nature of the solution obtained usually requires additional analysis. For some problems, the solution can be identified as the global optimum solution, that is, the solution that maximizes or minimizes the objective function over all feasible solutions. For other problems, the solution can only be identified as a local optimum, that is, a solution better than all feasible points in the close neighborhood of the solution. Because of numerical difficulties associated with the procedure, it is even possible that the Solver may fail to find a local optimum. We leave these questions to more advanced texts on nonlinear programming. Here we describe the operation of the add-in when the Nonlinear item on the OR_MM menu is selected.

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Operations Research Models and Methods
by Paul A. Jensen
Copyright 2004 - All rights reserved