Abstract
In this paper, 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.
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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.
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.
Giannessi, F., Theorems of the Alternative and Optimality Conditions, Journal of Optimization Theory and Applications, Vol. 42, pp. 331–365, 1984.
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.
Mangasarian, O. L., Nonlinear Programming, McGraw-Hill, New York, New York, 1969.
Bazaraa, M. S., and Shetty, C. M., Foundations of Optimization, Springer, Berlin, Germany, 1976.
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Bigi, G., Pappalardo, M. Regularity Conditions for the Linear Separation of Sets. Journal of Optimization Theory and Applications 99, 533–540 (1998). https://doi.org/10.1023/A:1021738714110
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DOI: https://doi.org/10.1023/A:1021738714110