Journal of Convex Analysis 18 (2011), No. 4, 915--947
Copyright Heldermann Verlag 2011
Subgradients of Minimal Time Functions Under Minimal Requirements
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
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.
Keywords: Variational analysis and optimization, minimal time functions, Minkowski gauges, generalized differentiation, subdifferentials, normal cones.
MSC: 49J52, 49J53, 90C31
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