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Date Published:
31/08/2016
Online Published:
31/08/2016
Abstract Views: 208
Views PDF: 204
Views PDF: 204
Section
Natural Sciences Issue (Vietnamese)
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
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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.
Keywords
directionally convex function, directionally (convex) subdifferential, optimization problem
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
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.
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