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First-Order Conditions for C0,1 Constrained vector optimization

Author

Listed:
  • Ginchev Ivan

    (Department of Mathematics, Technical University of Varna, Bulgaria)

  • Guerraggio Angelo

    (Department of Economics, University of Insubria, Italy)

  • Rocca Matteo

    (Department of Economics, University of Insubria, Italy)

Abstract

For a Fritz John type vector optimization problem with C0,1 data we define different type of solutions, give their scalar characterizations applying the so called oriented distance, and give necessary and sufficient first order optimality conditions in terms of the Dini derivative. While establishing the sufficiency, we introduce new type of efficient points referred to as isolated minimizers of first order, and show their relation to properly efficient points. More precisely, the obtained necessary conditions are necessary for weakly efficiency, and the sufficient conditions are both sufficient and necessary for a point to be an isolated minimizer of first order.

Suggested Citation

  • Ginchev Ivan & Guerraggio Angelo & Rocca Matteo, 2003. "First-Order Conditions for C0,1 Constrained vector optimization," Economics and Quantitative Methods qf0307, Department of Economics, University of Insubria.
    • Handle: RePEc:ins:quaeco:qf0307
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    File URL: https://www.eco.uninsubria.it/RePEc/pdf/QF2003_19.pdf
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    References listed on IDEAS

    as
    1. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    2. La Torre Davide & Rocca Matteo, 2002. "C 1,1 functions and optimality conditions," Economics and Quantitative Methods qf0208, Department of Economics, University of Insubria.
    3. S. Bolintinéanu & M. El Maghri, 1998. "Second-Order Efficiency Conditions and Sensitivity of Efficient Points," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 569-592, September.
    4. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
    5. J. B. Hiriart-Urruty, 1979. "Tangent Cones, Generalized Gradients and Mathematical Programming in Banach Spaces," Mathematics of Operations Research, INFORMS, vol. 4(1), pages 79-97, February.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    vector optimization; nonsmooth optimization; C0; 1 functions; Dini derivatives; first-order optimality conditions; lagrange multipliers;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General

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