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

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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.

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Authors and Affiliations

  1. Faculty of Sciences (Mathematics), University of Pisa, Largo B. Pontecorvo 5, 56127, Pisa, Italy

    A. Moldovan

  2. Faculty of Sciences (Mathematics) and Faculty of Economics, University of Verona, Viale Università, Palazzina 32, 37129, Verona, Italy

    L. Pellegrini

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  1. A. Moldovan
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  2. L. Pellegrini
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Correspondence to L. Pellegrini.

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Communicated by F. Giannessi.

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Moldovan, A., Pellegrini, L. On Regularity for Constrained Extremum Problems. Part 2: Necessary Optimality Conditions. J Optim Theory Appl 142, 165–183 (2009). https://doi.org/10.1007/s10957-009-9521-8

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  • DOI: https://doi.org/10.1007/s10957-009-9521-8

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