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From: Brandon on 21 May 2010 15:17
Can the Matlab Optimization toolbox be used to solve maxmin problems?

I know the functions fminimax and fgoalattain are conceptually similar in that they solve the minimax problem so can either be implemented to solve maxmin problem?

Thanks in advance for your consideration.
From: Alan Weiss on 24 May 2010 07:56
On 5/21/2010 3:09 PM, Brandon wrote:
> Can the Matlab optimization toolbox be used to solve maxmin problems?
> I know the functions fminimax and fgoalattain are conceptually close (ie
> they solve the minimax problem) so can they be implemented in a way that
> solves the related maxmin problem?
>
> Thanks in advance for your consideration.

It depends what you mean. fminimax solves problems of the form
min_x max_i F_i(x)

This is the same as
-max_x min_i (-F_i(x))
So in that sense fminimax solves maxmin problems. But this might not be
a formulation you want. If you are more specific, we might be able to
help more.

Alan Weiss
MATLAB mathematical toolbox documentation
From: Brandon on 24 May 2010 14:21
Alan Weiss <aweiss(a)mathworks.com> wrote in message <htdpgr$8os$1(a)fred.mathworks.com>...
> On 5/21/2010 3:09 PM, Brandon wrote:
> > Can the Matlab optimization toolbox be used to solve maxmin problems?
> > I know the functions fminimax and fgoalattain are conceptually close (ie
> > they solve the minimax problem) so can they be implemented in a way that
> > solves the related maxmin problem?
> >
> > Thanks in advance for your consideration.
>
> It depends what you mean. fminimax solves problems of the form
> min_x max_i F_i(x)
>
> This is the same as
> -max_x min_i (-F_i(x))
> So in that sense fminimax solves maxmin problems. But this might not be
> a formulation you want. If you are more specific, we might be able to
> help more.
>
> Alan Weiss
> MATLAB mathematical toolbox documentation

Hello Alan. Thank you for your thoughtful response.

The problem I am trying to solve is:

max_x min_i F_i(x)

So, if I understand your response correctly, passing -F_i(x) into fminimax will give me the solution to the problem I restated above. Correct? Of course, it seems the caveat is that the value of the final objective function (vector) will be reversed.

I checked this approach with some code and it seems to give me what I expect for simple cases.
From: Alan Weiss on 24 May 2010 14:54
On 5/24/2010 2:21 PM, Brandon wrote:
> Alan Weiss <aweiss(a)mathworks.com> wrote in message
> <htdpgr$8os$1(a)fred.mathworks.com>...
>> On 5/21/2010 3:09 PM, Brandon wrote:
>> > Can the Matlab optimization toolbox be used to solve maxmin problems?
>> > I know the functions fminimax and fgoalattain are conceptually close
>> (ie
>> > they solve the minimax problem) so can they be implemented in a way
>> that
>> > solves the related maxmin problem?
>> >
>> > Thanks in advance for your consideration.
>>
>> It depends what you mean. fminimax solves problems of the form
>> min_x max_i F_i(x)
>>
>> This is the same as
>> -max_x min_i (-F_i(x))
>> So in that sense fminimax solves maxmin problems. But this might not
>> be a formulation you want. If you are more specific, we might be able
>> to help more.
>>
>> Alan Weiss
>> MATLAB mathematical toolbox documentation
>
> Hello Alan. Thank you for your thoughtful response.
> The problem I am trying to solve is:
>
> max_x min_i F_i(x)
>
> So, if I understand your response correctly, passing -F_i(x) into
> fminimax will give me the solution to the problem I restated above.
> Correct? Of course, it seems the caveat is that the value of the final
> objective function (vector) will be reversed.
>
> I checked this approach with some code and it seems to give me what I
> expect for simple cases.

You understood perfectly what I said, and, yes, you need to take the
negative of the final answer. I'm glad I was able to help.

Alan Weiss
MATLAB mathematical toolbox documentation
From: Brandon on 24 May 2010 15:20
Alan Weiss <aweiss(a)mathworks.com> wrote in message <htei1j$pjn$1(a)fred.mathworks.com>...
> On 5/24/2010 2:21 PM, Brandon wrote:
> > Alan Weiss <aweiss(a)mathworks.com> wrote in message
> > <htdpgr$8os$1(a)fred.mathworks.com>...
> >> On 5/21/2010 3:09 PM, Brandon wrote:
> >> > Can the Matlab optimization toolbox be used to solve maxmin problems?
> >> > I know the functions fminimax and fgoalattain are conceptually close
> >> (ie
> >> > they solve the minimax problem) so can they be implemented in a way
> >> that
> >> > solves the related maxmin problem?
> >> >
> >> > Thanks in advance for your consideration.
> >>
> >> It depends what you mean. fminimax solves problems of the form
> >> min_x max_i F_i(x)
> >>
> >> This is the same as
> >> -max_x min_i (-F_i(x))
> >> So in that sense fminimax solves maxmin problems. But this might not
> >> be a formulation you want. If you are more specific, we might be able
> >> to help more.
> >>
> >> Alan Weiss
> >> MATLAB mathematical toolbox documentation
> >
> > Hello Alan. Thank you for your thoughtful response.
> > The problem I am trying to solve is:
> >
> > max_x min_i F_i(x)
> >
> > So, if I understand your response correctly, passing -F_i(x) into
> > fminimax will give me the solution to the problem I restated above.
> > Correct? Of course, it seems the caveat is that the value of the final
> > objective function (vector) will be reversed.
> >
> > I checked this approach with some code and it seems to give me what I
> > expect for simple cases.
>
> You understood perfectly what I said, and, yes, you need to take the
> negative of the final answer. I'm glad I was able to help.
>
> Alan Weiss
> MATLAB mathematical toolbox documentation

Thank you for lending your expertise to my problem. ~Cheers, Brandon
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