Abstract
In the field of constrained optimization the nonvacuity or the boundedness of the generalized Lagrange multiplier set is guaranteed under some regularity conditions (or constraint qualification; the difference in the terminology consisting of whether or not the condition involves the objective function). This type of analysis is now-a-days well stated also for nondifferenti able optimization. Moreover, the great development of these topics has been enforced with the recent results that establish strict relationships between regularity conditions (as well as metric regularity) and calmness, exact penalization and stability. The nature of all these conditions is of analytical type. On the other hand, a new approach has been recently proposed for establishing regularity conditions. It mainly exploits geometrical tools and takes into account that regularity conditions for optimality can be expressed as geometrical conditions for certain types of separation or more generally they are conditions which guarantee the impossibility of a system. This paper aims to give a characterization of regularity conditions for generalized systems and to apply it to the study of optimality conditions.
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© 1996 Springer Science+Business Media New York
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Castellani, M., Mastroeni, G., Pappalardo, M. (1996). On Regularity for Generalized Systems and Applications. In: Di Pillo, G., Giannessi, F. (eds) Nonlinear Optimization and Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0289-4_2
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DOI: https://doi.org/10.1007/978-1-4899-0289-4_2
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