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Topic: Specialized Linear Program
Replies: 4   Last Post: Apr 27, 2013 9:38 AM

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Posts: 12,067
Registered: 7/15/05
Re: Specialized Linear Program
Posted: Apr 25, 2013 10:23 PM
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quasi wrote:
>analyst41 wrote:
>>Max sum over j, c(j).x(j)
>> sum over j, a(i,j).x(j) <= b(i) for i = 1,2,..m.
>> x(j) >= 0 for j = 1,2,...n.
>>All a's,b's and c's are >= 0.
>>This LP has the property that x feasible implies x' feasible
>>whenever 0 <= x'(j) <= x(j) for all j.
>>Are these problems any easier than general LPs?

>Not as far as I can see.
>The only difference is that you have a known vertex of the
>feasible region, namely the origin, and that the feasible region
>is entirely in the first orthant.

Forget the first orthant part -- that's automatic just from
x(j) >= 0 for all j.

>Given any LP with a known vertex of the feasible region, a
>change of coordinates can be used to achieve another LP
>in the form you specify above.

I'm not so sure about the above.

Maybe there's some advantage after all.


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