Abstract
In this paper we study a special minimal time function, given with respect to a set of directions. Several properties, concerning continuity, convexity, Lipschitz behaviour and subdifferential calculus are explored. An application to a vectorial location problem is provided.
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Acknowledgements
The authors thank to one of the reviewers for some remarks which improved the presentation of the paper.
Disclosure statement
No potential conflict of interest was reported by the authors.
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Funding
The work of M. Durea was supported by a grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-ID-PCE-2011-3-0084, contract number 239/05.10.2011. The work of M. Panţiruc was supported by Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-RU-TE-2014-4-0019. The work of R. Strugariu was partially supported by the strategic grant POSDRU/159/1.5/S/133652, co-financed by the European Social Fund within the Sectorial Operational Program Human Resources Development 2007-2013, and partially supported by a grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-ID-PCE-2011-3-0563, contract number 343/05.10.2011.