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Operations Research Models and Methods
Problems Section
Problems for Nonlinear Programming Models
 - Nonlinear Variations on a Linear Program

a. For convenience express the objective as a minimization and add the cost of additional plant use.

To determine the effect of the addition we note that the nonlinear terms are separable and all of the same form. To determine the convexity we compute the second derivative.

Since this is negative, the minimization objective is not convex and the algorithm does not yield a global minimum.

The constraints of the problem must also be modified to account for the increased production.

b. We restate the constraint as a greater than or equal to constraint, and we compute the Hessian matrix for the quadratic.

The matrix is positive definite, and the constraint is convex. The solution will be a global minimum.

c. This is a nonlinear equality constraint. The fact that it is an equality constraint makes the feasible region nonconvex. The solution therefore may be a local minimum.

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Operations Research Models and Methods
by Paul A. Jensen
Copyright 2001 - All rights reserved