MaplePrimes - answers and comments on Question, The least of a function

Maple's bugs

Kitonum — Wed, 18 Jan 2012 19:40:54 Z

Checked the calculation of the minimum by the second method. The result again is false:

Maple will return the first local minimum

dskoog — Wed, 18 Jan 2012 20:17:26 Z

When you use the Optimization:-Minimize command, Maple returns the first local minimum it finds in the interval and will NOT return the global minimum for the equation.

In this case:

[-2.02634418581704, [x = .452809600260151]]

is correct because it corresponds to the first local minimum.

As pagan mentions, you can also use the method=branchandbound method or by inspection, you can also find this manually by specifying the range in which you expect to see the min:

For example:

Optimization[Minimize](h(x),x=0.8..1.4);

returns:

[-4.57468789382248, [x = 1.14302017080379]] which is the result that you were expecting for your particular problem (Note though that this may NOT be the global min).

Hope this helps.

Maple's bug

Kitonum — Wed, 18 Jan 2012 23:13:05 Z

The apparent error of Maple! I did the same example using the command Optimization [Minimize] . The result is also wrong!

local vs global

pagan — Wed, 18 Jan 2012 20:15:50 Z

You obtained a local minimum, and you did not specify a global method.

restart:	

h:=x->1+2*cos(2*x)+3*cos(4*x)+4*cos(8*x):

Optimization[Minimize](h(x),x=-Pi/12..5*Pi/12,method=branchandbound);

                 [-4.57468789382248, [x = 1.14302016898108]]

As the previous comments, there is a known

dskoog — Thu, 19 Jan 2012 00:02:35 Z

As the previous comments suggest, there is a known bug within the minimize command for the given function. However, the result from the Optimization[Minimize] command is expected.

From the Optimization, Minimize help page: The Minimize command computes a LOCAL minimum of an objective function. In this case, Minimize finds a local minimum at: [-2.02634418581704, [x = .452809600260151]] and stops searching there.

If you tell Optimization[Minimize] to look at another specific interval, it will find the first local minimum and return that value (this was shown in my second example above).

The difference here is that the minimize command symbolically searches for a GLOBAL minmum, whereas the Optimization[Minimize] command returns the first LOCAL minimum it encounters within a certain range.