| DIFFERENTIABILITY OF CONVEX FUNCTIONS ON SUBLINEAR TOPOLOGICAL SPACES AND VARIATIONAL PRINCIPLES IN LOCALLY CONVEX SPACES |
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| 引用本文： | CHENG Lixin,TENG Yanmei. DIFFERENTIABILITY OF CONVEX FUNCTIONS ON SUBLINEAR TOPOLOGICAL SPACES AND VARIATIONAL PRINCIPLES IN LOCALLY CONVEX SPACES[J]. 数学年刊B辑(英文版), 2005, 26(4): 611-632 |
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| 作者姓名： | CHENG Lixin TENG Yanmei |
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| 作者单位： | CHENG LIXIN TENG YANMEI Department of Mathematic，Xiamen University，Xiamen 361005，Fujian，China. Department of Mathematic，Beihang University，Beijing 100083，China. |
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| 基金项目： | Project supported by the National Natural Science Foundation of China (No.10471114)the Pujian Provincial Natural Science Foundation of China (No.F00021)the Tianyuan Foundation of Mathematics (No,A0324618). |
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| 摘 要： | This paper presents a type of variational principles for real valued w lower semicon-tinuous functions on certain subsets in duals of locally convex spaces, and resolve a problem concerning differentiability of convex functions on general Banach spaces. They are done through discussing differentiability of convex functions on nonlinear topological spaces and convexification of nonconvex functions on topological linear spaces.
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| 关 键 词： | Convex function βdifferentiability Variationsl principle Perturbed optimization Banach spaces Locally convex spaces |
| 收稿时间： | 2022-03-04 |
DIFFERENTIABILITY OF CONVEX FUNCTIONS ON SUBLINEAR TOPOLOGICAL SPACES AND VARIATIONAL PRINCIPLES IN LOCALLY CONVEX SPACES |
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| CHENG Lixin and TENG Yanmei. DIFFERENTIABILITY OF CONVEX FUNCTIONS ON SUBLINEAR TOPOLOGICAL SPACES AND VARIATIONAL PRINCIPLES IN LOCALLY CONVEX SPACES[J]. Chinese Annals of Mathematics,Series B, 2005, 26(4): 611-632 |
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| Authors: | CHENG Lixin and TENG Yanmei |
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| Affiliation: | [1]Department of Mathematic, Xiamen University, Xiarnen 361005, Fujian, China. [2]Department of Mathematic, Beihang University, Beijing 100083, China. |
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| Abstract: | This paper presents a type of variational principles for real valued w lower semicon-tinuous functions on certain subsets in duals of locally convex spaces, and resolve a problem concerning differentiability of convex functions on general Banach spaces. They are done through discussing differentiability of convex functions on nonlinear topological spaces and convexification of nonconvex functions on topological linear spaces. |
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| Keywords: | Convex function βdifferentiability Variational principle Perturbed optimization Banach spaces Locally convex spaces |
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