As shown in Figure 2, the situation is slightly more complex for constrained optimization problems. The presence of a constraint boundary, in Figure 2 in the form of a simple bound on the permitted values of the control variable, can cause the global minimum to be an extreme value, an extremum (i.e., an endpoint), rather than a true stationary point. Some methods of treating constraints transform the optimization problem into an equivalent unconstrained one, with a different objective function. Such techniques are discussed in Section .
Figure 2: Types of Minima for Constrained Optimization Problems.