Have a personal or library account? Click to login
Hahn-Banach-Type Theorems and Subdifferentials for Invariant and Equivariant Order Continuous Vector Lattice-Valued Operators with Applications to Optimization Cover

Hahn-Banach-Type Theorems and Subdifferentials for Invariant and Equivariant Order Continuous Vector Lattice-Valued Operators with Applications to Optimization

By: Antonio Boccuto  
Open Access
|Jan 2022

References

  1. [1] ALIPRANTIS, CH. D.—BURKINSHAW, O.: Positive Operators, Springer, Dordrecht, 2006.10.1007/978-1-4020-5008-4
  2. [2] ASDRUBALI, F.—BALDINELLI, G.—BIANCHI, F.—COSTARELLI, D.—ROTILI, A.—SERACINI, M.—VINTI, G.: Detection of thermal bridges from thermographic images by means of image processing approximation algorithms, Appl. Math. Comput. 317 (2018), 160–171.10.1016/j.amc.2017.08.058
  3. [3] BAZARAA, M. S.—SHERALI, H. D.—SHETTY, C. M.: Nonlinear Programming. Theory and Algorithms. Wiley-Interscience, John Wiley & Sons, Inc., Hoboken, New Jersey, 2006.10.1002/0471787779
  4. [4] BOCCUTO, A.: Hahn-Banach-type theorems and applications to optimization for partially ordered vector space-valued invariant operators, Real Anal. Exchange 44 (2019), no. 2, 333–368.10.14321/realanalexch.44.2.0333
  5. [5] BOCCUTO, A.: Hahn-Banach and sandwich theorems for equivariant vector latticevalued operators and applications, Tatra Mt. Math. Publ. 76 (2020), 11–34.10.2478/tmmp-2020-0015
  6. [6] BOCCUTO, A.—CANDELORO, D.: Sandwich theorems, extension principles and amenability, Atti Sem. Mat. Fis. Univ. Modena 42 (1994), 257–271.
  7. [7] BOCCUTO, A.—CANDELORO, D.: Integral and Ideals in Riesz Spaces, Inform. Sci.179 (2009), no. 2, 891–2902.10.1016/j.ins.2008.11.001
  8. [8] BOCCUTO, A.—GERACE, I.—GIORGETTI, V.: A blind source separation technique for document restoration, SIAM J. Imaging Sciences 12 (2019), no. 2, 1135–1162.10.1137/18M1188793
  9. [9] CANDELORO, D.—MESIAR, R.—SAMBUCINI, A. R.: A special class of fuzzy measures: Choquet integral and applications, Fuzzy Sets Systems 355 (2019), 83–99.10.1016/j.fss.2018.04.008
  10. [10] CHOJNACKI, W.: Sur un théorème de Day, un théorème de Mazur-Orlicz et une généralisation de quelques théorèmes de Silverman, Colloq. Math. 50 (1986), 257–262.10.4064/cm-50-2-257-262
  11. [11] CLUNI, F.—COSTARELLI, D.—MINOTTI, A.M.—VINTI, G.: Enhancement of thermographic images as tool for structural analysis in earthquake engineering, NDT & E International 70 (2015), no. 4, 60—72.10.1016/j.ndteint.2014.10.001
  12. [12] COSTARELLI, D.—SERACINI, M.—VINTI, G.: A segmentation procedure of the pervious area of the aorta artery from CT images without contrast medium, Math. Methods Appl. Sci. 43 (2020), no. 1, 114–133.10.1002/mma.5838
  13. [13] EATON, M.L.: Group Invariance Applications in Statistics. In: NSF-CBMS Regional Conference Series in Probability and Statistics Vol.1, Institute of Mathematical Statistics, Hayward, CA, 1989.10.1214/cbms/1462061029
  14. [14] GOODFELLOW, I.—BENGIO, Y.—COURVILLE, A.: Deep Learning, MIT Press, Cambridge, MA, 2016.
  15. [15] ELSTER, K.-H.—NEHSE, R.: Necessary and sufficient conditions for the order-completeness of partially ordered vector spaces, Math. Nachr. 81 (1978), 301–311.10.1002/mana.19780810116
  16. [16] KUSRAEV, A. G.—KUTATELADZE, S.S.: Subdifferentials: Theory and applications. Kluwer Academic Publ., Dordrecht, 1995.10.1007/978-94-011-0265-0
  17. [17] KUTATELADZE, S.S.: Boolean models and simultaneous inequalities, Vladikavkaz Math. J. 11 (2009), no. 3, 44–50.
  18. [18] KUTATELADZE, S.S.: The Farkas lemma revisited, Sibirsk. Mat. Zh. 51 (2020), no. 1, 98—109. (In Russian); Sib. Math. J. 51 (2010), no. 1, 78–87. (English translation)
  19. [19] LUXEMBURG, W. A.J.—MASTERSON, J.J.: An extension of the concept of the order-dual of a Riesz space, Canad. J. Math. 19 (1976), 488–498.10.4153/CJM-1967-041-6
  20. [20] LUXEMBURG, W. A. J.—ZAANEN, A.C.: Riesz Spaces. I. North-Holland Publ. Co., Amsterdam, 1971.
  21. [21] MANGASARIAN, O. L.: Nonlinear Programming, McGraw-Hill Book Co., New York, 1969.
  22. [22] PATERSON, A.L.T.: Amenability. Amer. Math. Soc., Providence, Rhode Island, 1988.
  23. [23] PERESSINI, A. L.: Ordered Topological Vector Spaces. Harper & Row, New York, 1967.
  24. [24] PFLUG, G. CH.—RŐMISCH, W.: Modeling, Measuring and Managing Risk. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2007.10.1142/6478
  25. [25] SAMBUCINI, A. R.: The Choquet integral with respect to fuzzy measures and applications, Math. Slovaca 67 (2017), no. 6, 1427–1450.10.1515/ms-2017-0049
  26. [26] SILVERMAN, R.: Invariant means and cones with vector interiors, Trans. Amer. Math. Soc. 88 (1958), no. 1, 75–79.10.1090/S0002-9947-1958-0095414-6
  27. [27] SILVERMAN, R.—YEN, T.: Addendum to: Invariant means and cones with vector interiors, Trans. Amer. Math. Soc. 88 (1958), no. 2, 327–330.10.1090/S0002-9947-1958-0095415-8
  28. [28] ZOWE, J.: A duality theorem for a convex programming problem in order complete vector lattices, J. Math. Anal. Appl. 50 (1975), 273–287.10.1016/0022-247X(75)90022-0
  29. [29] ZOWE, J.: The saddle point theorem of Kuhn and Tucker in ordered vector spaces, J. Math. Anal. Appl. 57 (1977), 41–55.10.1016/0022-247X(77)90283-9
  30. [30] ZOWE, J.: Sandwich theorems for convex operators with values in an ordered vector space, J. Math. Anal. Appl. 66 (1978), 282–296.10.1016/0022-247X(78)90232-9
DOI: https://doi.org/10.2478/tmmp-2021-0010 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195
Language: English
Page range: 139 - 156
Submitted on: Dec 1, 2020
Published on: Jan 1, 2022
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2022 Antonio Boccuto, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.