On the Positive Definiteness of Limiting Coderivative for Set-Valued Mappings
On the Positive Definiteness of Limiting Coderivative for Set-Valued Mappings
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DOI：
10.1007/s11228-020-00547-z
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发表时间：
2020-07
影响因子：
1.6
通讯作者：
T. Nghia;D. Pham;T. T. T. Tran-T.-T.
中科院分区：
文献类型：
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作者：
T. Nghia;D. Pham;T. T. T. Tran-T.-T.
本文讨论了Mordukhovich和Nghia(SIAM J.Optim.26,1032-1059,2016，猜想3.6)所怀疑的集值映射的极限余导数的正定性和局部强极大单调性之间的相互联系。我们用一个反例证明了这个猜想是正确的，并提供了一些特殊的类来证明它是正确的。然而，极限余导数的正定性刻画了一种称为近强单调性的新性质。从而证明了在极限余导数为正定的条件下，集值映射的强度量正则性是成立的。
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.