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

A. Moldovan () and L. Pellegrini ()
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A. Moldovan: University of Pisa
L. Pellegrini: University of Verona

Journal of Optimization Theory and Applications, 2009, vol. 142, issue 1, No 9, 165-183

Abstract: 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.

Keywords: Image space; Constraint qualifications; Regularity conditions; Calmness; Metric regularity (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (32)

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DOI: 10.1007/s10957-009-9521-8

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