Abstract
The main aspect of the paper consists in the application of a particular theorem of separation between two sets to the image associated with a constrained extremum problem. In the image space, the two sets are a convex cone, which depends on the constraints (equalities or inequalities) of the given problem, and its image. In this way, a condition for the existence of a regular saddle point (i.e., a sufficient optimality condition) is obtained. This regularity condition is compared with those existing in the literature.
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Moldovan, A., Pellegrini, L. On Regularity for Constrained Extremum Problems. Part 1: Sufficient Optimality Conditions. J Optim Theory Appl 142, 147–163 (2009). https://doi.org/10.1007/s10957-009-9518-3
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DOI: https://doi.org/10.1007/s10957-009-9518-3