This paper is devoted to the study of directional minimal time functions that specify the minimal time for a vector to reach an object following its given direction. We provide a careful analysis of general and generalized differentiation properties of this class of functions. The analysis allows us to study a new model of facility location that involves sets.
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The research of Nguyen Mau Nam was partially supported by the Simons Foundation under grant #208785.
The research of C. Zalinescu was supported by the grant PN-II-ID-PCE-2011-3-0084, CNCS-UEFISCDI, Romania.
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Nam, N.M., Zălinescu, C. Variational Analysis of Directional Minimal Time Functions and Applications to Location Problems. Set-Valued Var. Anal 21, 405–430 (2013). https://doi.org/10.1007/s11228-013-0232-9
- Directional minimal time functions
- Scalarization functions
- Generalized differentiation
- Facility location problems