On the Positive Definiteness of Limiting Coderivative for Set-Valued Mappings
| Autor: | D. T. Pham, Tran T. A. Nghia, T. T. T. Tran |
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| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Numerical Analysis Pure mathematics 021103 operations research Conjecture Property (philosophy) Applied Mathematics Mathematics::Optimization and Control 0211 other engineering and technologies Monotonic function 010103 numerical & computational mathematics 02 engineering and technology Limiting 01 natural sciences Set (abstract data type) Positive definiteness Metric (mathematics) Geometry and Topology 0101 mathematics Analysis Mathematics Counterexample |
| Zdroj: | Set-Valued and Variational Analysis. 29:283-300 |
| ISSN: | 1877-0541 1877-0533 |
| DOI: | 10.1007/s11228-020-00547-z |
| Popis: | This paper concerns the interconnection between the positive definiteness of limiting coderivative and the local strong maximal monotonicity of set-valued mappings suspected in Mordukhovich and Nghia (SIAM J. Optim. 26, 1032–1059, 2016, Conjecture 3.6). We disprove the conjecture by a counterexample and provide some special classes at which it is true. However, the positive definiteness of limiting coderivative characterizes a new property called nearly strong monotonicity. Consequently, we show that the strong metric regularity of set-valued mappings could be obtained under the positive definiteness of limiting coderivative. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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