Assume the optimal value of a primal problem is bounded. Is the following statement true?
- If the primal problem is bounded, then its dual problem is bounded as well.
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Sign up to join this communityAssume the optimal value of a primal problem is bounded. Is the following statement true?
No. The primal LP min $x+y$ subject to $x-y\ge 0$ has no bounded objective.
Instead, one must assume boundedness of the primal and dual problem as a hypothesis, and then gets the result that both problems are solvable and their values agree.