Lipschitz properties of nonsmooth functions and set-valued mappings via generalized differentiation |
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| Affiliation: | 1. Robert H. Smith School of Business, University of Maryland, College Park, MD 20742, USA;2. Department of Management Information Science, University of Siegen, 57068, Siegen, Germany;3. Center for Advanced Studies in Management (CASiM), HHL, 04109, Leipzig, Germany;4. Leeds School of Business, University of Colorado, Boulder, CO, 80303, USA |
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| Abstract: | In this paper, we revisit the Mordukhovich subdifferential criterion for Lipschitz continuity of nonsmooth functions and the coderivative criterion for the Aubin/Lipschitz-like property of set-valued mappings in finite dimensions. The criteria are useful and beautiful results in modern variational analysis showing the state of the art of the field. As an application, we establish necessary and sufficient conditions for Lipschitz continuity of the minimal time function and the scalarization function, which play an important role in many aspects of nonsmooth analysis and optimization. |
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| Keywords: | Lipschitz property Generalized differentiation Subdifferential Coderivative Minimal time function Scalarization function |
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