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Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

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Open Access Research Article

On the separation of sets

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pp. 1819–1824Vol. 29Issue 6June 2026DOI: 10.47974/JIM-2264XML
Received:
01 Feb 2025
Published Online:
05 Mar 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2264
Pages:
1819–1824

Abstract

The concepts of separability, proper separability, and strict separability and related concepts are considered in this paper. Some properties of these sets are proved, and applications are considered.

Keywords

Subject Classifications

03C1552B4054D65

References

[1] C. D. Aliprantis and K. C. Border, Infinite Dimensional Analysis: A Hitchhiker’s Guide, 3rd ed., Springer, Berlin-Heidelberg-New York (2006). 
[2] V. G. Boltyanski, H. Martini, and P. Soltan, Excursions into Combinatorial Geometry, Springer, Berlin-Heidelberg-New York (1997). 
[3] S. Boyd, L. Vandenberghe, Convex Optimization, Cambridge University Press, Cambridge (2004). 
[4] C. J. Goh and X. Q. Yang, Duality in Optimization and Variational Inequalities, Taylor & Francis, London-New York (2002). 
[5] B. Grünbaum, Convex Polytopes, 2nd ed., Springer, New York-Berlin-Heidelberg (2003). 
[6] L. Narici and E. Beckenstein, Topological Vector Spaces, 2nd ed., Chapman and Hall / CRC Press, Boca Raton (2010). 
[7] A. G. Ramm, P. N. Shivakumar, and A. V. Strauss (eds.), Operator Theory and Its Applications, American Mathematical Society, Providence (2000). 
[8] R. T. Rochafellar, Convex Analysis, Princeton University Press, Princeton (1970). 
[9] H. H. Schaefer and M. P. Wolff, Topological Vector Spaces, 2nd ed., Springer, New York (1999). 
[10] S. M. Stefanov, “Valid inequalities and cutting planes for some polytopes,” Mathematical Inequalities and Applications, vol. 1, no. 2, pp. 285-294 (1998). 
[11] S. M. Stefanov, Convex Separable Programming, Kluwer Academic Publishers, Dordrecht (2000). 
[12] S. M. Stefanov, Separable Programming: Theory and Methods, Kluwer Academic Publishers, Dordrech-Boston-London (2001). 
[13] S. M. Stefanov, “Valid inequalities, cutting planes and integrality of the knapsack polytope,” Journal of Interdisciplinary Mathematics, vol. 14, no. 4, pp. 389-406 (2011). 
[14] S. M. Stefanov, “On the solution of quadratic programming problem with a feasible region defined as a Minkowski sum of a compact set and finitely generated convex closed cone,” Journal of Information and Optimization Sciences, vol. 39, no. 6, pp. 1223-1230 (2018). 
[15] S. M. Stefanov, Separable Optimization: Theory and Methods, Springer, Cham (2021). 
[16] S. M. Stefanov, “Continuous linear knapsack problems revisited,” Journal of Information and Optimization Sciences, vol. 44, no. 5, pp. 909-922 (2023). 
[17] S. M. Stefanov, “Numerical solution of box constrained separable convex quadratic programming problems,” Journal of Information and Optimization Sciences, vol. 45, no. 1, pp. 57-71 (2024). 
[18] S. M. Stefanov, “On the properties of cones and polar cones,” Journal of Interdisciplinary Mathematics, (2026), doi: 10.47974/JIM-2262.  

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