A New Nonsmooth Bundle-Type Approach for a Class of Functional Equations in Hilbert Spaces
A new bundle-type approach for solving a class of functional equations is presented by combining bundle idea for nonsmooth optimization with common iterative process for functional equations. Our strategy is to approximate the nonsmooth function in functional equation by a sequence of convex piecewi...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2017/3941084 |
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| _version_ | 1832559285857419264 |
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| author | Jie Shen Miao Tian Fang-Fang Guo Jun-Nan Zhang |
| author_facet | Jie Shen Miao Tian Fang-Fang Guo Jun-Nan Zhang |
| author_sort | Jie Shen |
| collection | DOAJ |
| description | A new bundle-type approach for solving a class of functional equations is presented by combining bundle idea for nonsmooth optimization with common iterative process for functional equations. Our strategy is to approximate the nonsmooth function in functional equation by a sequence of convex piecewise linear functions, as in the bundle method; this makes the problem more tractable and reduces the difficulty of implementation of method. We only require the piecewise linear convex approximate functions, rather than the actual function, to satisfy the uniform boundedness condition with respect to one variable at stability centers. One example is given to demonstrate the application of the proposed method. |
| format | Article |
| id | doaj-art-724494991c374115baa88363bad228f1 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-724494991c374115baa88363bad228f12025-02-03T01:30:27ZengWileyJournal of Function Spaces2314-88962314-88882017-01-01201710.1155/2017/39410843941084A New Nonsmooth Bundle-Type Approach for a Class of Functional Equations in Hilbert SpacesJie Shen0Miao Tian1Fang-Fang Guo2Jun-Nan Zhang3School of Mathematics, Liaoning Normal University, Dalian 116029, ChinaSchool of Mathematics, Liaoning Normal University, Dalian 116029, ChinaSchool of Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaSchool of Mathematics, Liaoning Normal University, Dalian 116029, ChinaA new bundle-type approach for solving a class of functional equations is presented by combining bundle idea for nonsmooth optimization with common iterative process for functional equations. Our strategy is to approximate the nonsmooth function in functional equation by a sequence of convex piecewise linear functions, as in the bundle method; this makes the problem more tractable and reduces the difficulty of implementation of method. We only require the piecewise linear convex approximate functions, rather than the actual function, to satisfy the uniform boundedness condition with respect to one variable at stability centers. One example is given to demonstrate the application of the proposed method.http://dx.doi.org/10.1155/2017/3941084 |
| spellingShingle | Jie Shen Miao Tian Fang-Fang Guo Jun-Nan Zhang A New Nonsmooth Bundle-Type Approach for a Class of Functional Equations in Hilbert Spaces Journal of Function Spaces |
| title | A New Nonsmooth Bundle-Type Approach for a Class of Functional Equations in Hilbert Spaces |
| title_full | A New Nonsmooth Bundle-Type Approach for a Class of Functional Equations in Hilbert Spaces |
| title_fullStr | A New Nonsmooth Bundle-Type Approach for a Class of Functional Equations in Hilbert Spaces |
| title_full_unstemmed | A New Nonsmooth Bundle-Type Approach for a Class of Functional Equations in Hilbert Spaces |
| title_short | A New Nonsmooth Bundle-Type Approach for a Class of Functional Equations in Hilbert Spaces |
| title_sort | new nonsmooth bundle type approach for a class of functional equations in hilbert spaces |
| url | http://dx.doi.org/10.1155/2017/3941084 |
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