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Rockafellian relaxation and minimum-norm slack for the Walrasian equilibrium problem

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  • Julio Deride

Abstract

We propose a Rockafellian relaxation of the Walrasian equilibrium problem for an exchange economy that may not admit one. Market clearing is slackened by a non-negative variable $v$ whose norm is penalized; the relaxation is well posed throughout. As the penalty grows, the residual converges to a vector $v^*_\infty$ of minimum norm in the feasible range of excess demand, measuring the distance to the nearest equilibrium-admitting economy. A stressed Shapley--Shubik example recovers the analytical infeasibility floor to machine

Suggested Citation

  • Julio Deride, 2026. "Rockafellian relaxation and minimum-norm slack for the Walrasian equilibrium problem," Papers 2607.04717, arXiv.org.
    • Handle: RePEc:arx:papers:2607.04717
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    File URL: https://arxiv.org/pdf/2607.04717
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