Minimal time function with respect to a set of directions: basic properties and applications

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.

Keywords:

• minimal time function
• convexity
• Lipschitz properties
• subdifferential calculus

AMS Subject Classification:

• 49J53
• 49K27
• 90C46

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.

Additional information

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.