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In this paper, a theory of lexicographic optimization for convex and compact feasible sets is presented. Existence, globality, unimodality, and uniqueness of the solution to the problem are proved. Also, necessary and sufficient conditions are derived that establish the relationship between the lexicographic problem and the maxmin problem. This framework is shown to be useful in the problem of designing flow control protocols. Towards this objective, a theory of bottleneck ordering is introduced, which unveils the convergence properties of the flow control problem.