A New Nonsmooth Bundle-Type Approach for a Class of Functional Equations in Hilbert Spaces
| Autor: | Jie Shen, Miao Tian, Fang-Fang Guo, Jun-Nan Zhang |
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| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Journal of Function Spaces, Vol 2017 (2017) |
| Druh dokumentu: | article |
| ISSN: | 2314-8896 2314-8888 |
| DOI: | 10.1155/2017/3941084 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
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