On the extreme points of the sets
*Stefan M. StefanovCorresponding authorstefm@swu.bgDepartment of InformaticsNeofit Rilski South-West UniversityBlagoevgrad, 2700, BulgariaView full profile →
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- Received:
- 01 Apr 2025
- Published Online:
- 01 Apr 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2388
- Pages:
- 1–7
Abstract
Keywords
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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, 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 Unoversity Press, Princeton (1970).
[9] H. H. Schaefer and M. P. Wolff, Topological Vector Spaces, 2nd ed., Springer, New York (1999).
[10] V. Soltan, “Support and separation properties of convex sets in finite dimension”, Extracta Mathematicae, vol. 36, no. 2, pp. 241-278 (2021).
[11] S. M. Stefanov, “Valid inequalities and cutting planes for some polytopes”, Mathematical Inequalities and Applications, vol. 1, no. 2, pp. 285-294 (1998).
[12] S. M. Stefanov, Convex Separable Programming, Kluwer Academic Publishers, Dordrecht (2000).
[13] S. M. Stefanov, Separable Programming: Theory and Methods, Kluwer Academic Publishers, Dordrech–Boston–London (2001).
[14] 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).
[15] 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).
[16] S. M. Stefanov, Separable Optimization: Theory and Methods, Springer, Cham (2021).
[17] S. M. Stefanov, “Continuous linear knapsack problems revisited”, Journal of Information and Optimization Sciences, vol. 44, no. 5, pp. 909-922 (2023).
[18] S. M. Stefanov, “On the separation of sets”, Journal of Interdisciplinary Mathematics, published online.
[19] S. M. Stefanov, “Supporting hyperplanes and separation of sets”, Journal of Interdisciplinary Mathematics, to appear.




