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A nonconvex separation property and some applications

Abstract

In this paper we proved a nonconvex separation property for general sets which coincides with the Hahn-Banach separation theorem when sets are convexes. Properties derived from the main result are used to compute the subgradient set to the distance function in special cases and they are also applied to extending the Second Welfare Theorem in economics and proving the existence of singular multipliers in Optimization.

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Correspondence to Alejandro Jofré.

Additional information

This work was partially supported by FONDECYT, ICM Complex Engineering System, CEE-ECOS.

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Jofré, A., Cayupi, J. A nonconvex separation property and some applications. Math. Program. 108, 37–51 (2006). https://doi.org/10.1007/s10107-006-0703-y

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Keywords

  • Variational analysis
  • Subgradient set
  • Nonconvex separation
  • Singular multiplier
  • Equilibrium price
  • Pareto optimum