The example provided here makes the Lagrangian relaxation (LR) not a mystery for me any more. Each step becomes very clear. I have read a lot of materials in LR. This is one of the best for beginners to get to know how LR works.
An implementation of LR with C++ in ILOG CPLEX can be found here.
That makes me think that there is probably no really unsolvable problems. It is just we haven't found a right way to approach it.
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