Minimal Time Functions and the Smallest Intersecting Ball Problem with Unbounded Dynamics

Nguyen Mau Nam (), Maria Cristina Villalobos () and Nguyen Thai An ()
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Nguyen Mau Nam: University of Texas-Pan American
Maria Cristina Villalobos: University of Texas-Pan American
Nguyen Thai An: Hue University

Journal of Optimization Theory and Applications, 2012, vol. 154, issue 3, No 3, 768-791

Abstract: Abstract The smallest enclosing circle problem introduced in the nineteenth century by Sylvester asks for the circle of smallest radius enclosing a given set of finite points in the plane. An extension of this problem, called the smallest intersecting ball problem, was also considered recently: given a finite number of nonempty closed subsets of a normed space, find a ball with the smallest radius that intersects all of the sets. In this paper, we initiate the study of minimal time functions generated by unbounded dynamics and discuss their applications to further extensions of the smallest enclosing circle problem. This approach continues our effort in applying convex and nonsmooth analysis to the well-established field of facility location.

Keywords: Minimal time functions; Subdifferential; Subgradient method; Smallest intersecting ball problem; 1-Center problem (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-012-0048-z

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