Question: Optimization and bounds on the variables

I'm doing some experimenting with the Optimization:-Maximize and Minimize functions, and I'm having difficulties getting them to find the actual extrema within a set of bounds.  I have found that the extrema they identify depend on the bounds, even when the same extrema lie within those bounds. I've also tried the initialpoint option to start the solution near the extrema and I've found three things: sometimes it works to get the correct solution, sometimes it doesn't and sometimes I get a message saying the initial point was ignored by the solver.

The problems I'm using are all taken from the Maple help or tutorials.

I haven't included a bunch of test cases but I've attached the Maple Flow file.  I have a suspicion it has to do with the second derivatives of the functions near the boundaries, but I'm not sure.

Can anyone point me to more information, or am I doing something wrong?

Thanks for your help.

Optimization_Local_Max_and_Min.flow