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| DIFFERENTIABILITY OF CONVEX FUNCTIONS ON SUBLINEAR TOPOLOGICAL SPACES AND VARIATIONAL PRINCIPLES IN LOCALLY CONVEX SPACES |
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Citation： |
CHENG Lixin,TENG Yanmei.DIFFERENTIABILITY OF CONVEX FUNCTIONS ON SUBLINEAR TOPOLOGICAL SPACES AND VARIATIONAL PRINCIPLES IN LOCALLY CONVEX SPACES[J].Chinese Annals of Mathematics B,2005,26(4):611~632 |
| Page view： 1332
Net amount： 1060 |
Authors： |
CHENG Lixin; TENG Yanmei |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.10471114), the Fujian Provincial Natural Science Foundation of China (No.F00021) and the Tianyuan Foundation of Mathematics (No.A0324618). |
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| Abstract： |
This paper presents a type of variational principles for real valued w^? lower semicontinuous 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. |
Keywords： |
Convex function, β differentiability, Variational principle, Perturbed optimization, Banach spaces, Locally convex spaces |
Classification： |
26E15, 46B20, 46G05 |
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