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Necessary and sufficient conditions for emptiness of the cones of generalized support vectors

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Abstract

The purpose of the paper is to establish the conditions which are necessary and sufficient for the cones of generalized (strong, strict) support vectors of a set in a finite-dimensional Euclidean space to be empty. In the present paper, an application of the proposed in J Optim Theory Appl (Gabidullina, J. Optim. Theory Appl. 158(1), 145–171, 2013) linear separability criterion for verification on emptiness or non-emptiness of the cones of GSVs (generalized support vectors) is also studied. We carry out the complete degeneracy analysis of the cones of GSVs for the different kinds of nonempty sets of Euclidean space. We present the different applications of the degeneracy analysis of the cones of GSVs as well.

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Acknowledgments

The author thanks Associated Editor and two anonymous Referees for their helpful comments and remarks on a previous version of the paper.

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  1. Department of Data Analysis and Operations Research, Kazan Federal University, 18, Kremljovskaja street, Kazan, 420008, Russia

    Z. R. Gabidullina

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  1. Z. R. Gabidullina
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Correspondence to Z. R. Gabidullina.

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Gabidullina, Z.R. Necessary and sufficient conditions for emptiness of the cones of generalized support vectors. Optim Lett 9, 693–729 (2015). https://doi.org/10.1007/s11590-014-0771-5

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