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Geometric Interpretation

There is a geometric interpretation of the conditions an optimal solution must satisfy. If we graph Example 1.1.2, we get a picture like that in Figure 1.1.

Figure 1.1: Geometric interpretation

Now, examine the gradients of f and g at the optimum point. They must point in the same direction, though they may have different lengths. This implies:


which, along with the feasibility of tex2html_wrap_inline427 , is exactly the condition tex2html_wrap_inline445 of Case (ii).

Michael A. Trick
Mon Aug 24 14:26:21 EDT 1998