Tell me more ×
Computational Science Stack Exchange is a question and answer site for scientists using computers to solve scientific problems. It's 100% free, no registration required.
up vote 0 down vote favorite

Assume we are given a linear programming problem. It is well-known that a linear programming problem is unbounded iff there exists an EXTREME direction $d$ such that cd>0 (consider maximization case). Now, I want to check whether my LP is unbounded. I described the existence of a recession direction in the feasible area of the given linear programming problem using constraints 2,3 and constraint (1) is for unboundedness.

1) $cd>0$;

2) $Ad \leq 0$;

3) $Bd \leq 0$;

After checking the feasibility of the above polyhedral, I have two directions. First, the polyhedral is infeasible. In this case for sure the problem is bounded (Since I could not find any feasible and also basic feasible solution for the corresponding LP). Second, what if the polyhedral is feasible? Then, can I say that I have an EXTREME ray $d$ with $cd>0$ ?

share|improve this question
You shouldn't use this site for posing theoretical questions that have no computational aspect. – Arnold Neumaier Jul 18 '12 at 14:49
You may want to post this on the Math SE site. – Paul♦ Jul 19 '12 at 14:34

closed as off topic by Arnold Neumaier, Aron Ahmadia Jul 18 '12 at 18:52

Questions on Computational Science Stack Exchange are expected to relate to computational science within the scope defined in the FAQ. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about closed questions here.