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Unformatted text preview: ( µ ) := max x∈ X L( x, µ ) . The concavity property always holds for (10), which often (but not always) makes this problem easy to solve. There are then methods to transform this dual solution to an approximate primal feasible solution. Weak duality states q* ≤ f * , and in general IP’s strong duality ( q * = f * ) cannot be expected. The advantage of Lagrange relaxation is that one can relax certain constraints and keep others in the underlying space and always receive a lower bound on the optimal value to the original (primal) problem. Each configuration will yield a different duality gap. A special case of Lagrangian relaxation is LP relaxation of an ILP, where the integrality condition is removed and the resulting LP is solved. Again, since the feasible set is expanded, this solution bounds the optimal value of the ILP from below. This weak duality property suggests that a dual heuristic is promising to use in an optimal method.
3.1.2. Optimal methods Optimal methods guarantee finding the optimal solution. An initial approach to trying to find an...
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