Thanh bên bài viết

PDF
Ngày xuất bản: 13/12/2024
Số lượt xem tóm tắt: 2
Số lượt xem PDF: 5
DOI: https://doi.org/10.52714/dthu.14.5.2025.1401
Số xuất bản
Tập 14 Số 5 (2025): Chuyên san Khoa học Tự nhiên (Tiếng Anh)
Chuyên mục
Khoa học Tự nhiên (Tiếng Anh)
Trích dẫn bài báo
Vo, D. T., & Huynh, N. C. (2024). Subdifferentials with degrees of freedom and applications to optimization problems. Tạp chí Khoa học Đại học Đồng Tháp, 14(5), 12-19. https://doi.org/10.52714/dthu.14.5.2025.1401

Subdifferentials with degrees of freedom and applications to optimization problems

Vo Duc Thinh1, , Huynh Ngoc Cam1
1 Faculty of Mathematics - Informatics Teacher Education, School of Education, Dong Thap University, Cao Lanh 870000, Vietnam

Nội dung chính của bài viết

Tóm tắt

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.

Chi tiết bài viết

Creative Commons License

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

Từ khóa

Computation rule, generalized convex function, subdifferential, optimality condition

Tài liệu tham khảo

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