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arXiv · 2509.18073

Pareto-Optimal Linear Programming

Bart van Rossum·Twan Dollevoet
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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.

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Bart van Rossum, Twan Dollevoet. 2025-09-22. Pareto-Optimal Linear Programming. https://arxiv.org/abs/2509.18073

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