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Date Published: 13/12/2024
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DOI: https://doi.org/10.52714/dthu.14.5.2025.1401
Issue
Vol. 14 No. 5 (2025): Natural Sciences Issue (English)
Section
Natural Sciences Issue (English)
How to Cite
Vo, D. T., & Huynh, N. C. (2024). Subdifferentials with degrees of freedom and applications to optimization problems. Dong Thap University Journal of Science, 14(5), 12-19. https://doi.org/10.52714/dthu.14.5.2025.1401

Subdifferentials with degrees of freedom and applications to optimization problems

Duc Thinh Vo1, , Ngoc Cam Huynh1
1 Faculty of Mathematics - Informatics Teacher Education, School of Education, Dong Thap University, Cao Lanh 870000, Vietnam

Main Article Content

Abstract

In this work, we first present a new class of generalized differentials, namely subdifferentials with degrees of freedom as well as their applications in nonsmooth optimization problems. We then establish some computation rules for subdifferentials with degree of frecdom of functions under basic qualification constraints. By using these computation rules, we provide necessary and sufficient conditions for unconstraint optmization problems and for optimization problems with geometric constraints.

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Keywords

Computation rule, generalized convex function, subdifferential, optimality condition

References

Ansari, Q. H. and Lalitha, C. S., & Mehta, M. (2014). Generalized convexity, nonsmooth variational inequalities and nonsmooth optimization, CRC Press, Taylor and Francis Group.
Bauschke, H. H., & Combettes, P. L. (2017). Convex analysis and monotone operator theory in Hilbert spaces, 2nd edition. Springer, New York.
Clarke, F. H., (1983), Optimization and nonsmooth analysis, Wiley-Interscience, New York.
Lara, F., & Marcavillaca, R. T. (2024). Bregman proximal point type algorithms for quasiconvex minimization, Optimization, 73, pp. 497–515.
Lara, F., & Kabgani, A. (2021). On Global Subdifferentials with Applications in Nonsmooth Optimization, Journal of Global Optimization, vol. 81, pp. 881–900.
Lara, F. (2022). On strongly quasiconvex functions: existence results and proximal point algorithms, J. Optim. Theory Appl., vol. 192, pp. 891–911.
Kabgani, A., & Lara, F. (2022). Strong subdifferentials: Theory and applications in nonconvex optimization, Journal of Global Optimization, vol. 84, pp. 349–368.
Mordukhovich, B. S., & Nam, N. M. (2014). An easy path to convex analysis and applications, Morgan & Claypool Publishers, Willistion.
Rockafellar, R. T. (1996). Convex analysis, Princeton University Press, Princeton, N.J.
Thinh, V. D., & Cam, H. N. (2024), Derivative with degree of freedom of multifunctions and applications, Dong Thap University Journal of Sciences, 13(2), 116-120. https://doi.org/10.52714/dthu.13.2.2024.1241

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