×

Regularity conditions for the linear separation of sets. (English) Zbl 0911.90297

Summary: We study the linear separation between a set and a convex cone. We introduce the concepts of regularity and total regularity of the separation with respect to a face of the cone and we give theorems characterizing them.

MSC:

90C30 Nonlinear programming
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Castellani, M., Mastroeni, G., and Pappalardo, M., On Regularity for Generalized Systems and Applications, Nonlinear Optimization and Applications, Edited by G. Di Pillo and F. Giannessi, Plenum Press, New York, pp. 13–26, 1996. · Zbl 0976.90101
[2] Castellani, M., Mastroeni, G., and Pappalardo, M., Separation of Sets, Lagrange Multipliers, and Totally Regular Extremum Problems, Journal of Optimization Theory of Applications, Vol. 92, pp. 249–261, 1997. · Zbl 0886.90127 · doi:10.1023/A:1022698811948
[3] Giannessi, F., Theorems of the Alternative and Optimality Conditions, Journal of Optimization Theory and Applications, Vol. 42, pp. 331–365, 1984. · Zbl 0504.49012 · doi:10.1007/BF00935321
[4] Quang, P. H., and Yen, N. D., New Proof of a Theorem of F. Giannessi, Journal of Optimization Theory and Applications, Vol. 68, pp. 385–387, 1991. · Zbl 0697.49022 · doi:10.1007/BF00941576
[5] Mangasarian, O. L., Nonlinear Programming, McGraw-Hill, New York, New York, 1969.
[6] Bazaraa, M. S., and Shetty, C. M., Foundations of Optimization, Springer, Berlin, Germany, 1976. · Zbl 0334.90049
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.