The Fenchel Duality Theorem in Fréchet Spaces
We generalize the Fenchel duality and inf-convolution theorems from convex optimization to Fréchet spaces. Our approach is simple and direct, and is to first prove a more general theorem in which we consider only one function and replace the product of spaces by an arbitrary Fréchet space. These res...
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1990
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sg-smu-ink.lkcsb_research-32082016-03-12T01:23:33Z The Fenchel Duality Theorem in Fréchet Spaces RODRIGUES, Brian We generalize the Fenchel duality and inf-convolution theorems from convex optimization to Fréchet spaces. Our approach is simple and direct, and is to first prove a more general theorem in which we consider only one function and replace the product of spaces by an arbitrary Fréchet space. These results extend those obtained recently by Attouch and Brezis. Applications of our Generalizations are given. 1990-01-01T08:00:00Z text https://ink.library.smu.edu.sg/lkcsb_research/2209 info:doi/10.1080/02331939008843516 https://doi.org/10.1080/02331939008843516 Research Collection Lee Kong Chian School Of Business eng Institutional Knowledge at Singapore Management University Locally convex space Fréchet space fully barreled Legendbe-Fenchel transform inf-convolution effective domain proper function sublevel set slater con-straint condition subdifferential normal cone tangent cone Kuhn-Tucker condition Mathematics Operations and Supply Chain Management |
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English |
| topic |
Locally convex space Fréchet space fully barreled Legendbe-Fenchel transform inf-convolution effective domain proper function sublevel set slater con-straint condition subdifferential normal cone tangent cone Kuhn-Tucker condition Mathematics Operations and Supply Chain Management |
| spellingShingle |
Locally convex space Fréchet space fully barreled Legendbe-Fenchel transform inf-convolution effective domain proper function sublevel set slater con-straint condition subdifferential normal cone tangent cone Kuhn-Tucker condition Mathematics Operations and Supply Chain Management RODRIGUES, Brian The Fenchel Duality Theorem in Fréchet Spaces |
| description |
We generalize the Fenchel duality and inf-convolution theorems from convex optimization to Fréchet spaces. Our approach is simple and direct, and is to first prove a more general theorem in which we consider only one function and replace the product of spaces by an arbitrary Fréchet space. These results extend those obtained recently by Attouch and Brezis. Applications of our Generalizations are given. |
| format |
text |
| author |
RODRIGUES, Brian |
| author_facet |
RODRIGUES, Brian |
| author_sort |
RODRIGUES, Brian |
| title |
The Fenchel Duality Theorem in Fréchet Spaces |
| title_short |
The Fenchel Duality Theorem in Fréchet Spaces |
| title_full |
The Fenchel Duality Theorem in Fréchet Spaces |
| title_fullStr |
The Fenchel Duality Theorem in Fréchet Spaces |
| title_full_unstemmed |
The Fenchel Duality Theorem in Fréchet Spaces |
| title_sort |
fenchel duality theorem in fréchet spaces |
| publisher |
Institutional Knowledge at Singapore Management University |
| publishDate |
1990 |
| url |
https://ink.library.smu.edu.sg/lkcsb_research/2209 https://doi.org/10.1080/02331939008843516 |
| _version_ |
1770570168567595008 |