Article Sidebar
Date Published:
31/08/2016
Online Published:
31/08/2016
Abstract Views: 45
Views PDF: 71
Views PDF: 71
Section
Natural Sciences Issue
How to Cite
Nguyen, T. T. T., & Vo, D. T. (2016). Directional (convex) subdifferential and applications. Dong Thap University Journal of Science, 21, 72-77. https://doi.org/10.52714/dthu.21.8.2016.379
Directional (convex) subdifferential and applications
Main Article Content
Abstract
In this paper, we introduce some properties of directionally convex functions and the directionally (convex) subdifferentials. Then, we apply results of the directionally subdifferentials to characterize necessary and sufficient conditions for solutions of an optimization problem.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Keywords
directionally convex function, directionally (convex) subdifferential, optimization problem
References
[1]. A. Bressan (1987), “Directional convexity and finite optimality conditions”, Journal of Mathematical Analysis and Applications, (125), p. 234-246.
[2]. J. V. Burke and R. A. Poliquin (1992), “Optimality conditions for non-finite valued convex composite functions”, Mathematical Programming, (57), p. 103-120.
[3]. E. Casas and F. Troltzsch (1999), “Second order necessary optimality conditions for some state-constrained control problems of semilinear elliptic equations”, Journal of Applied Mathematics & Optimization, (39), p. 211-227.
[4]. A. Dhara and J. Dutta (2012), Optimality conditions in convex optimization, CRC Press.
[5]. A. L. Dontchev and R. T. Rockafellar (1996), “Characterization of strong regularity for variational inequalities over polyhedral convex sets”, SIAM Journal on Control and Optimization, (6), p. 1087-1105.
[6]. R. Janin and J. Gauvin (1999), “Lipschitz-type stability in nonsmooth convex programs”,SIAM Journal on Control and Optimization, (38), p. 124-137.
[7]. T. Munakata and S. Kaneko (1976), “Directional convexity and the directional discrete maximum principle sfor quantized control system”, Keio Engineering Reports, 29 (2), p. 7-12.
[8]. R. T. Rockafellar (1960), Convex analysis, Princeton University Press.
[2]. J. V. Burke and R. A. Poliquin (1992), “Optimality conditions for non-finite valued convex composite functions”, Mathematical Programming, (57), p. 103-120.
[3]. E. Casas and F. Troltzsch (1999), “Second order necessary optimality conditions for some state-constrained control problems of semilinear elliptic equations”, Journal of Applied Mathematics & Optimization, (39), p. 211-227.
[4]. A. Dhara and J. Dutta (2012), Optimality conditions in convex optimization, CRC Press.
[5]. A. L. Dontchev and R. T. Rockafellar (1996), “Characterization of strong regularity for variational inequalities over polyhedral convex sets”, SIAM Journal on Control and Optimization, (6), p. 1087-1105.
[6]. R. Janin and J. Gauvin (1999), “Lipschitz-type stability in nonsmooth convex programs”,SIAM Journal on Control and Optimization, (38), p. 124-137.
[7]. T. Munakata and S. Kaneko (1976), “Directional convexity and the directional discrete maximum principle sfor quantized control system”, Keio Engineering Reports, 29 (2), p. 7-12.
[8]. R. T. Rockafellar (1960), Convex analysis, Princeton University Press.
Most read articles by the same author(s)
- Thi Tran Chau Pham, Duc Thinh Vo, Thi Kim Yen Ngo, Thuy Hoang Yen Tran, The level-set method combined with Desmos software to orient the solution of inequality problems , Dong Thap University Journal of Science: Vol. 11 No. 1 (2022): Social Sciences and Humanities Issue (Vietnamese)
- Thi My Dung Nguyen, Thi Thanh Thảo Nguyen, Solutions to improve professional capacity for Information Technology Faculty in the context of Industrial Revolution 4.0 in Dong Thap University , Dong Thap University Journal of Science: Vol. 9 No. 6 (2020): Social Sciences and Humanities Issue (Vietnamese)
- Ngoc Cam Huynh, Duc Thinh Vo, K-coincidence point without commutative condition in partially ordered metric , Dong Thap University Journal of Science: Vol. 12 No. 2 (2023): Natural Sciences Issue (Vietnamese)
- Ngoc Anh Tho Pham, Kim Yen Ngo Thi, Duc Thinh Vo, Thi Tran Chau Pham, Parabolic subdifferential and its applications to optimality conditions , Dong Thap University Journal of Science: Vol. 12 No. 2 (2023): Natural Sciences Issue (Vietnamese)
- Thi Tran Chau Pham, Duc Thinh Vo, Thi Kim Yen Ngo, Thuy Hoang Yen Tran, Procedures to build some inequality problems from basic convex functions , Dong Thap University Journal of Science: Vol. 11 No. 4 (2022): Social Sciences and Humanities Issue (Vietnamese)
- Dr. Duc Thinh Vo, Ngoc Cam Huynh, Derivatives with degree of freedom of multifunctions and application , Dong Thap University Journal of Science: Vol. 13 No. 2 (2024): Natural Sciences Issue (Vietnamese)
- Van Dung Nguyen, Trung Hieu Nguyen, Duc Thinh Vo, Công bố khoa học của Trường Đại học Đồng Tháp giai đoạn 2003-2013 và đề xuất một số định hướng , Dong Thap University Journal of Science: No. 9 (2014): Part A - Social Sciences and Humanities
- Duc Thinh Vo, The directionally normal cone and optimal condition , Dong Thap University Journal of Science: No. 13 (2015): Part B - Natural Sciences
- Thi Bich Van Dang, Duc Thinh Vo, Generalized Studniarski derivatives and its applications , Dong Thap University Journal of Science: No. 31 (2018): Part B - Natural Sciences
- Thi Kim Loan Huynh, Duc Thinh Vo, Cones generated by semi-infinite systems and their applications on optimization , Dong Thap University Journal of Science: Vol. 9 No. 5 (2020): Natural Sciences Issue (English)