Relaxation

Abstract

An optimization problem asks for a solution from a given feasible domain that provides the optimal value of a given objective function. The technique of relaxation is, contrary to the technique of restriction, to relax some constraints on the feasible solutions and, hence, enlarge the feasible domain so that an optimal or a good approximate solution to the relaxed version of the problemcan be found in polynomial time. This optimal or approximate solution to the relaxed version is not necessarily feasible for the original problem, and we may need to modify it to get a feasible solution to the original input. This modification step often requires special tricks and is an important part of the relaxation technique.