The main aspect of the paper consists in the application of a particular theorem of separation between two suitable 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 kind of conditions (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.
On Regularity for Constrained Extremum Problems. Part I: Sufficient Optimality Conditions
PELLEGRINI, Letizia
2009-01-01
Abstract
The main aspect of the paper consists in the application of a particular theorem of separation between two suitable 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 kind of conditions (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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