Abstract

This paper concerns the study of a broad class of minimal time functions corresponding to control problems with constant convex dynamics and closed target sets in arbitrary Banach spaces. In contrast to other publications, we do not impose any nonempty interior and/or calmness assumptions on the initial data and deal with generally non-Lipschitzian minimal time functions. The major results present refined formulas for computing various subgradients of minimal time functions under minimal requirements in both cases of convex and nonconvex targets. Our technique is based on advanced tools of variational analysis and generalized differentiation.

Author information

Contact details are reproduced from the original publication and may be historical.

Boris S. Mordukhovich

Dept. of Mathematics, Wayne State University, Detroit, MI 48202, U.S.A.

boris@math.wayne.edu

Nguyen Mau Nam

Dept. of Mathematics, The University of Texas – Pan American, Edinburg, TX 78539–2999, U.S.A.

nguyenmn@utpa.edu

Keywords

  • Variational analysis and optimization
  • minimal time functions
  • Minkowski gauges
  • generalized differentiation
  • subdifferentials
  • normal cones

Mathematics Subject Classification

49J52, 49J53, 90C31

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Suggested citation

B. S. Mordukhovich, N. M. Nam. “Subgradients of Minimal Time Functions Under Minimal Requirements.” Journal of Convex Analysis 18 (2011), No. 4, 915–947. https://doi.org/10.68381/jca18058

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Published by Heldermann Verlag, 2011. Rights now held by Banach Press LLC.