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.

中文翻译：

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集值映射的极限代码导数的正定性

本文涉及限制coderivative的正定性和在Mordukhovich和Nghia酒店（SIAM J.的Optim。疑似集值映射的局部强最大单调性之间的互连26，1032至1059年，2016年，猜想3.6）。我们通过一个反例来反驳这个猜想，并提供了一些特殊的类来证明它是正确的。但是，限制代码导数的正定性是一种称为近强单调性的新属性。因此，我们表明可以在限制代码导数的正定性下获得强的集值映射的度量规则性。