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

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quasi

Posts: 10,188
Registered: 7/15/05
Re: Specialized Linear Program
Posted: Apr 25, 2013 10:23 PM
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analyst41 wrote:
>
>Max sum over j, c(j).x(j)
>St
> 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.

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.

quasi



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