The search results
are shown below. The process immediately moves to the negative
quadrant and the objective becomes a large negative value.
We have discovered a region of the variable space that has
an unbound objective value. The minimum found by the Gradient
method was a local minimum point. There is no global minimum,
because the objective function is unbounded from below. The
cubic terms in the function definition cause this result.
The program recognizes the unboundedness when
the search coordinates go beyond the limits expressed in the
parameters. The termination message shows the following.
The previously discovered local minimum can be
found by the conjugate gradient method by reducing the maximum
step size of the Golden Section line search method. The following
result was obtained by reducing the maximum step size from
5 to 1.
The solution is obtained with only
four line searches and a much smaller number of functional
evaluations than required for the gradient method. |