Some properties of second-order weak subdifferentials

This article deals with second-order weak subdifferential. Firstly, the concept of second-order weak subdifferential is defined. Next, some of its properties are investigated. The necessary and sufficient condition for a second-orderweakly subdifferentiable function to have a global minimum has been proved. It has been proved that a second-orderweakly subdifferentiable function is both lower semicontinuous and lower Lipschitz.

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