Abstract
The paper contains applications of variational analysis to the study of Pareto optimality in nonconvex economies with infinite-dimensional commodity spaces satisfying the Asplund property. Our basic tool is a certain extremal principle that provides necessary conditions for set extremality and can be treated as a variational extension of the classical convex separation principle to systems of nonconvex sets. In this way we obtain new versions of the generalized second welfare theorem for nonconvex economies in terms of appropriate normal cones of variational analysis.
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Malcolm, G.G., Mordukhovich, B.S. Pareto Optimality in Nonconvex Economies with Infinite-dimensional Commodity Spaces. Journal of Global Optimization 20, 323–346 (2001). https://doi.org/10.1023/A:1017978215263
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DOI: https://doi.org/10.1023/A:1017978215263