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linear programming

 
 
eric
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      06-20-2011
Dear c++ or advanced computer scienctist or mathmatician:
on the book(Introduction to Algorithms 3rd ed) page 851, chapter 29
Linear Programming
I ask one of that book's author:
-----------------------------------------------
dear thomas:

the the end of that page

if a linear program has some feasible solutions but does not have a
finite optimal objective value, we say that the linear program is
unbounded

but
you want us to prove in Exercise 29.1-9
to show
that a linear program can have a finite optimal objective value even
if
the feasible region is not bounded

which is very unlogical for me

looking to hear from you soon
Eric

------------------------------------------------------------------

Eric, you'll have to think outside the box just a little bit. It may
seem illogical, but there's a simple solution.

Tom Cormen
Professor and Chair
Dartmouth College Department of Computer Science
http://www.cs.dartmouth.edu/~thc/
-----------------------------------------------------
but I still not figure out
plz give hint/suggestion/advice, thank your help/effort/time a lot in
advance, Eric
 
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Alf P. Steinbach /Usenet
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      06-20-2011
* eric, on 20.06.2011 05:53:
> Dear c++ or advanced computer scienctist or mathmatician:
> on the book(Introduction to Algorithms 3rd ed) page 851, chapter 29
> Linear Programming
> I ask one of that book's author:
> -----------------------------------------------
> dear thomas:
>
> the the end of that page
>
> if a linear program has some feasible solutions but does not have a
> finite optimal objective value, we say that the linear program is
> unbounded
>
> but
> you want us to prove in Exercise 29.1-9
> to show
> that a linear program can have a finite optimal objective value even
> if
> the feasible region is not bounded
>
> which is very unlogical for me
>
> looking to hear from you soon
> Eric
>
> ------------------------------------------------------------------
>
> Eric, you'll have to think outside the box just a little bit. It may
> seem illogical, but there's a simple solution.
>
> Tom Cormen
> Professor and Chair
> Dartmouth College Department of Computer Science
> http://www.cs.dartmouth.edu/~thc/
> -----------------------------------------------------
> but I still not figure out
> plz give hint/suggestion/advice, thank your help/effort/time a lot in
> advance, Eric


Let

A = does not have finite objective value
B = is unbounded

One statement you're quoting is that A implies B.
This means that in every case where A is true, B will necessarily be true.
Another is that B does not imply A.
This means that in some cases where B is true, A is not true.

For example, if you're out in the rain without any protection, then you get wet.
And in some cases when you get wet, you are not out in the rain without protection.


Cheers & hth., and please post to a relevant group next time!,

- Alf

--
blog at <url: http://alfps.wordpress.com>
 
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eric
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      06-20-2011
On Jun 19, 11:36*pm, "Alf P. Steinbach /Usenet" <alf.p.steinbach
(E-Mail Removed)> wrote:
> * eric, on 20.06.2011 05:53:
>
>
>
> > Dear c++ or advanced computer scienctist or mathmatician:
> > * *on the book(Introduction to Algorithms 3rd ed) page 851, chapter29
> > Linear Programming
> > I ask one of that book's author:
> > -----------------------------------------------
> > * * dear thomas:

>
> > * *the the end of that page

>
> > * if a linear program has some feasible solutions but does not have a
> > * finite optimal objective value, we say that the linear program is
> > * unbounded

>
> > * but
> > * you want us to prove in Exercise 29.1-9
> > * to show
> > * that a linear program can have a finite optimal objective value even
> > if
> > * the feasible region is not bounded

>
> > * which is very unlogical for me

>
> > * looking to hear from you soon
> > * Eric

>
> > ------------------------------------------------------------------

>
> > Eric, you'll have to think outside the box just a little bit. *It may
> > seem illogical, but there's a simple solution.

>
> > Tom Cormen
> > Professor and Chair
> > Dartmouth College Department of Computer Science
> >http://www.cs.dartmouth.edu/~thc/
> > -----------------------------------------------------
> > but I still not figure out
> > plz give hint/suggestion/advice, thank your help/effort/time a lot in
> > advance, Eric

>
> Let
>
> * *A = does not have finite objective value
> * *B = is unbounded
>
> One statement you're quoting is that A implies B.
> This means that in every case where A is true, B will necessarily be true..
> Another is that B does not imply A.
> This means that in some cases where B is true, A is not true.
>
> For example, if you're out in the rain without any protection, then you get wet.
> And in some cases when you get wet, you are not out in the rain without protection.
>
> Cheers & hth., and please post to a relevant group next time!,
>
> - Alf
>
> --
> blog at <url:http://alfps.wordpress.com>


----------------------------------------------
I think you reply a little bit too fast.
Could I ask you, are you computer science/math student/worker?
in that book, that page, that sentence
there is no word(s) (implies)

which part do you think it can be treated as (implies)?
"We say" ?

why it can not be treated as (equal or defined it)

even that sentence should be treated as your way (implies) not
mine(equal)
then
Can you show out what is the definition of bounded or unbounded, /*
since we need that definition but authors did not gave out */?

looking to see any computer scientist/mathmatician 's advice/
suggestion/hint and thanks a lot in advance, Eric
 
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Alf P. Steinbach /Usenet
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      06-20-2011
* eric, on 20.06.2011 09:58:
> in that book, that page, that sentence
> there is no word(s) (implies)


"if" - "then" expresses an implication

use e.g. Wikipedia to learn about logical implications


cheers & hth., & please next time post in an appropriate group,

- alf

--
blog at <url: http://alfps.wordpress.com>
 
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gwowen
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      06-20-2011
On Jun 20, 7:36*am, "Alf P. Steinbach /Usenet" <alf.p.steinbach
(E-Mail Removed)> wrote:
> Let
>
> * *A = (the program) does not have finite objective value
> * *B = (the program) is unbounded
>
> One statement you're quoting is that A implies B.


That's not right. The statement he quotes gives B as the *definition*
of A, so A <=> B
 
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gwowen
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      06-20-2011
On Jun 20, 4:53*am, eric <(E-Mail Removed)> wrote:

> *if a linear program has some feasible solutions but does not have a
> *finite optimal objective value, we say that the linear program is
> *unbounded


Here, he's talking about the linear program being unbounded.

> if*the feasible region is not bounded


Here, he's talking about the feasible region being unbounded.
They're not the same thing.

Guru Meditation: Maximise (7-x) subject to (x>0).
 
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Paul
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      06-20-2011

"eric" <(E-Mail Removed)> wrote in message
news:(E-Mail Removed)...
> Dear c++ or advanced computer scienctist or mathmatician:
> on the book(Introduction to Algorithms 3rd ed) page 851, chapter 29
> Linear Programming
> I ask one of that book's author:
> -----------------------------------------------
> dear thomas:
>
> the the end of that page
>
> if a linear program has some feasible solutions but does not have a
> finite optimal objective value, we say that the linear program is
> unbounded
>
> but
> you want us to prove in Exercise 29.1-9
> to show
> that a linear program can have a finite optimal objective value even
> if
> the feasible region is not bounded
>
> which is very unlogical for me
>

Maybe a 'feasible region' is not bounded but the progam is bounded.

 
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Alf P. Steinbach /Usenet
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      06-20-2011
* gwowen, on 20.06.2011 12:07:
> On Jun 20, 7:36 am, "Alf P. Steinbach /Usenet"<alf.p.steinbach
> (E-Mail Removed)> wrote:
>> Let
>>
>> A = (the program) does not have finite objective value
>> B = (the program) is unbounded
>>
>> One statement you're quoting is that A implies B.

>
> That's not right. The statement he quotes gives B as the *definition*
> of A, so A<=> B


An "if-then" is a one way implication, not two-way.

For example, IF the text is so vague/informal as to not make that distinction,
THEN it's meaningless to ponder very fine details of meaning in the text.


Cheers & hth.,

- Alf

--
blog at <url: http://alfps.wordpress.com>
 
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gwowen
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      06-20-2011
On Jun 20, 1:09*pm, "Alf P. Steinbach /Usenet" <alf.p.steinbach
(E-Mail Removed)> wrote:

> > That's not right. *The statement he quotes gives B as the *definition*
> > of A, so A<=> *B

>
> An "if-then" is a one way implication, not two-way.


Usually yes. But this is phrased like'If "something" satifies
"condition A", then we say it is "A-ified".' In English-as-she-is-
used-by-mathematicians that's *a definition* of "A-ified". It's two
way. As a native English speaking mathematician, you really should
take me word on this.

e.g. Definition of continuity under arbitrary topologies: "If the
preimage under f() of any open set is itself, we say f() is
continuous".
 
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gwowen
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      06-20-2011
On Jun 20, 1:59*pm, gwowen <(E-Mail Removed)> wrote:

> e.g. Definition of continuity under arbitrary topologies: "If the
> preimage under f() of any open set is itself, we say f() is
> continuous".


Ooops missed a word ... e.g. Definition of continuity under arbitrary
topologies: "If the preimage under f() of any open set is itself open,
we say f() is continuous".

 
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