Pareto-Optimal Linear Programming

Abstract: Pareto-optimality plays a central role in evaluating the efficiency of solutions to allocation problems, such as house allocation, school choice, and kidney exchange. We introduce a general linear programming problem subject to Pareto-optimality conditions, which we call Max-Pareto. Using the novel result that Pareto-optimal bipartite matchings are fractionally Pareto-optimal, we prove that Max-Pareto is $\mathcal{NP}$-complete. We propose a bilinear programming formulation of Max-Pareto, and evaluate its computational performance on the problem of finding Pareto-optimal allocations of highest welfare.