Abstract
The optimality for a constrained extremum problem can be studied proving the disjunction between suitable subsets of the image space associated to the problem. This disjunction can be stated showing that these sets are linear or conically separated [1,2,3]. Under the “image regularity condition” (in short IRC) in [2], it has been proved the existence of generalized Karush—Kuhn—Tucker multipliers associated to a conic separation. Moreover it has been proved that IRC is equivalent to the calmness introduced by Clarke and the existence of an exact penalty function. Here we study the possibility of relating the local image regularity condition with a generic nonlinear separation not necessarily conic or linear and we provide refinements of some results obtained in [2].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
F. Giannessi, “Theorems of the Alternative and Optimality Conditions”, J.O.T.A., Vol. 42, N. 3, 1984, p. 331–365.
P. H. Dien, G. Mastroeni, M. Pappalardo, P. H. Quang, “Regularity conditions for constrained exteremum problems via image space: the nonlinear case; J.O.T.A., Vol. 80, N. 1, 1994, p. 19–37.
P. H. Dien, G. Mastroeni, M. Pappalardo, P. H. Quang, “Regularity conditions for constrained extremum problems via image space: the linear case” Springer Lectures Notes in Economics, Vol. 405, Komlosi-Rapcsak-Schaible (eds), 1994, pp. 145–153.
G. Mastroeni, “Regularity Properties of the Marginal Function Via Image Space”, Report N. 3.203(765), Dept. of Mathematics, University of Pisa, 1993.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Mastroeni, G., Pappalardo, M. (1998). Separation and regularity in the image space. In: Giannessi, F., Komlósi, S., Rapcsák, T. (eds) New Trends in Mathematical Programming. Applied Optimization, vol 13. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2878-1_14
Download citation
DOI: https://doi.org/10.1007/978-1-4757-2878-1_14
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4793-2
Online ISBN: 978-1-4757-2878-1
eBook Packages: Springer Book Archive