444 Nonlinear Programming III: Constrained Optimization Techniques
Figure 7.11 Aφfunction discontinuous forq=0.Figure 7.12 Derivatives of aφfunction discontinuous for 0< q <1.3.q=1. In this case, under certain restrictions, it has been shown by Zangwill
[7.16] that there exists anr 0 so large that the minimum ofφ(X, rk) s exactlyi
the constrained minimum of the original problem for allrk>r 0. However, the
contours of theφfunction look similar to those shown in Fig. 7.12 and possess
discontinuous first derivatives along the boundary. Hence despite the conve-
nience of choosing a single rk that yields the constrained minimum in one
unconstrained minimization, the method is not very attractive from computa-
tional point of view.