There are many ways to relax a problem, and we’ve seen three of the most important. The first, Constraint Relaxation, simply removes some constraints altogether and makes progress on a looser form of the problem before coming back to reality. The second, Continuous Relaxation, turns discrete or binary choices into continua: when deciding between iced tea and lemonade, first imagine a 50–50 “Arnold Palmer” blend and then round it up or down. The third, Lagrangian Relaxation, turns impossibilities into mere penalties, teaching the art of bending the rules (or breaking them and accepting the
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