quasi wrote: >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.
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.