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Stability of critical points for vector valued functions and Pareto efficiency

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  • Miglierina Enrico

    (Department of Economics, University of Insubria, Italy)

Abstract

In this work we consider the critical points of a vector-valued function f. We study their stability in order to obtain a necessary condition for Paret efficiency. We point out, by an example, that the classical notions of stability (concerning a single point) are not suitable in the settings. We use a stability notion for sets to prove that the counterimage of a minimal point for f is stable.This result is based on the study of a dynamical system defined by a differential inclusion. In the vector case this inclusion plays the same role as gradient system in the scalar setting.

Suggested Citation

  • Miglierina Enrico, 2003. "Stability of critical points for vector valued functions and Pareto efficiency," Economics and Quantitative Methods qf0301, Department of Economics, University of Insubria.
    • Handle: RePEc:ins:quaeco:qf0301
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    File URL: https://www.eco.uninsubria.it/RePEc/pdf/QF2003_1.pdf
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    References listed on IDEAS

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    1. Smale, Stephen, 1976. "Exchange processes with price adjustment," Journal of Mathematical Economics, Elsevier, vol. 3(3), pages 211-226, December.
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    3. Wan, Yieh-Hei, 1975. "On local Pareto optima," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 35-42, March.
    4. Simon, Carl P. & Titus, Charles, 1975. "Characterization of optima in smooth Pareto economic systems," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 297-330.
    5. Jörg Fliege & Benar Fux Svaiter, 2000. "Steepest descent methods for multicriteria optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(3), pages 479-494, August.
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