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## [Help-glpk] (no subject)

**From**: |
Cordian Riener |

**Subject**: |
[Help-glpk] (no subject) |

**Date**: |
Mon, 17 May 2004 22:47:18 +0200 (MEST) |

Hello,
I am faced with the following problem: I want to deside, if a point p is
inside a convex hull of given points q_j. I so have to calculate the
following LP:
x^(tr)*p -x[0] --> max
x^(tr)*q_j -x[0]<= 0 for all j and x^(tr) meaning the transpose of x
x^(tr)*p-x[0] <=1 (just to have an optimal value of the function)
So if p is inside q, the maximal value is 0 and it is acheafed only for all
x =0 if and only if p is not on a facette.
if p is on a facette the optimal value is of course 0 again, but there
should be another optimal sollution for the x.
My problem now is, tha the lp solver always stops, when the was found, that
there is no greater value than 0. But in order to also decide, if p is on a
facette, I should now, is there is another representation for this sollutin
that the trivial one, with all x=0. So my question is: Is the a possibility
to see, if, once the optimal value was found, the representaion is unique,
or if also other sollution exist.
Thanx for your help and best wishes fom Germany
Cordian
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