By minimizing the distance from the nominal parameter point (g12 = 1, g32g14 = -2) to the Hopf bifurcation line, the system can be made to lie on the boundary of the stable regime; see Figure 8. Table 1 shows the iteration counts required to obtain the result, using Sequential Quadratic Programming (SQP) with line-search [27]. Owing to the use of line-search, each optimization iteration entails a number of functional evaluations, this in turn requiring a number of one-parameter continuation iterations to find the (locally) closest point on Σ(ps). The optimality tolerance on the objective is set as 10-3 relative to its initial value and the relative parameter tolerance for approximating F(p) is set to 10-4. Clearly, the number of one-parameter continuations is significantly higher than the optimization iterations. Thus, for high dimensional examples it is important that the former can be carried out efficiently.