Example 5

This example has the same data as Example 4 except for $\,\alpha=0\,.$ Figure 9 indicates that the optimal control is bang-bang and satisfies the switching conditions inferred from (2.22),

$$\begin{eqnarray*} \hspace*{-8mm} \bar{u}(x) = \left \{ \begin{array}{llllll} u_1... ... & \,\mbox{if} & \;\; \bar{q}(x) > 0 \end{array}\right \} \,. \; \end{eqnarray*}$$

SNOPT fails for larger $N$ while LANCELOT needs excessive compute time. Figure 10 shows the associated adjoint variable and switching function.

Table 6: Information on solution of Example 5

N+1	it	LOQO	Acc	$F(\bar{y})$	SNOPT	MINOS	LANCELOT
50	37	145	8	.0539133	2399	205	923
100	60	5735	8	.0544745	f	4432	33390
200	84	137514	8	.0547818	f	119971	-