Error Bounds for Approximate Solutions of Abstract Inequality Systems and Infinite Systems of Inequalities on Banach Spaces
| Autor: | Mingwu Ye, Chong Li, Sy-Ming Guu, Jinhua Wang |
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| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Numerical Analysis Pure mathematics 021103 operations research Applied Mathematics 0211 other engineering and technologies Fréchet derivative Banach space 010103 numerical & computational mathematics 02 engineering and technology Function (mathematics) Derivative Lipschitz continuity 01 natural sciences Prime (order theory) symbols.namesake Simple (abstract algebra) symbols Geometry and Topology 0101 mathematics Newton's method Analysis Mathematics |
| Zdroj: | Set-Valued and Variational Analysis. 30:283-303 |
| ISSN: | 1877-0541 1877-0533 |
| DOI: | 10.1007/s11228-020-00551-3 |
| Popis: | Using the result of the error estimate of the simple extended Newton method established in the present paper for solving abstract inequality systems, we study the error bound property of approximate solutions of abstract inequality systems on Banach spaces with the involved function F being Frechet differentiable and its derivative $F^{\prime }$ satisfying the center-Lipschitz condition (not necessarily the Lipschitz condition) around a point x0. Under some mild conditions, we establish results on the existence of the solutions, and the error bound properties for approximate solutions of abstract inequality systems. Applications of these results to finite/infinite systems of inequalities/equalities on Banach spaces are presented and the error bound properties of approximate solutions of finite/infinite systems of inequalities/equalities are also established. Our results extend the corresponding results in [3, 18, 19]. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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