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On Regularity for Constrained Extremum Problems. Part 2: Necessary Optimality Conditions

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  • A. Moldovan

    (University of Pisa)

  • L. Pellegrini

    (University of Verona)

Abstract

A particular theorem for linear separation between two sets is applied in the image space associated with a constrained extremum problem. In this space, the two sets are a convex cone, depending on the constraints (equalities and inequalities) of the given problem and the homogenization of its image. It is proved that the particular linear separation is equivalent to the existence of Lagrangian multipliers with a positive multiplier associated with the objective function (i.e., a necessary optimality condition). A comparison with the constraint qualifications and the regularity conditions existing in the literature is performed.

Suggested Citation

  • A. Moldovan & L. Pellegrini, 2009. "On Regularity for Constrained Extremum Problems. Part 2: Necessary Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 165-183, July.
    • Handle: RePEc:spr:joptap:v:142:y:2009:i:1:d:10.1007_s10957-009-9521-8
    DOI: 10.1007/s10957-009-9521-8
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    References listed on IDEAS

    as
    1. R. I. Boţ & E. R. Csetnek & A. Moldovan, 2008. "Revisiting Some Duality Theorems via the Quasirelative Interior in Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 67-84, October.
    2. M. Chinaie & J. Zafarani, 2009. "Image Space Analysis and Scalarization of Multivalued Optimization," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 451-467, September.
    3. A. Moldovan & L. Pellegrini, 2009. "On Regularity for Constrained Extremum Problems. Part 1: Sufficient Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 147-163, July.
    4. K. Madani & G. Mastroeni & A. Moldovan, 2007. "Constrained Extremum Problems with Infinite-Dimensional Image: Selection and Necessary Conditions," Journal of Optimization Theory and Applications, Springer, vol. 135(1), pages 37-53, October.
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