Subdifferentials of a minimum time function in Banach spaces

In general Banach space setting, we study the minimum time function determined by a closed convex set K and a closed set S (this function is simply the usual Minkowski function of K if S is the singleton consisting of the origin). In particular we show that various subdifferentials of a minimum time function are representable by virtue of corresponding normal cones of sublevel sets of the function.

[1]  Lionel Thibault,et al.  On various notions of regularity of sets in nonsmooth analysis , 2002 .

[2]  Pierpaolo Soravia.  Generalized motion of a front propagating along its normal direction: a differential games approach , 1994 .

[3]  F. S. De Blasi,et al.  On a Generalized Best Approximation Problem , 1998 .

[4]  M. Fabian,et al.  Functional Analysis and Infinite-Dimensional Geometry , 2001 .

[5]  Chong Li,et al.  Derivatives of Generalized Distance Functions and Existence of Generalized Nearest Points , 2002, J. Approx. Theory.

[6]  Peter R. Wolenski,et al.  The subgradient formula for the minimal time function in the case of constant dynamics in Hilbert space , 2004, J. Glob. Optim..

[7]  M. Ferris,et al.  On the Clarke subdifferential of the distance function of a closed set , 1992 .

[8]  Yu. S. Ledyaev,et al.  Nonsmooth analysis and control theory , 1998 .

[9]  P. Wolenski,et al.  Proximal Analysis and the Minimal Time Function , 1998 .

[10]  Isao Nakayama,et al.  Uniqueness of Lower Semicontinuous Viscosity Solutions for the Minimum Time Problem , 2000, SIAM J. Control. Optim..

[11]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[12]  Pierpaolo Soravia,et al.  Discontinuous viscosity solutions to dirichlet problems for hamilton-jacob1 equations with , 1993 .

[13]  P. Wolenski,et al.  Variational Analysis for a Class of Minimal Time Functions in Hilbert Spaces , 2004 .

[14]  Chong Li,et al.  Constraint Qualification, the Strong CHIP, and Best Approximation with Convex Constraints in Banach Spaces , 2003, SIAM J. Optim..

[15]  F. Clarke,et al.  Proximal Smoothness and the Lower{C 2 Property , 1995 .

[16]  C. Zălinescu.  Convex analysis in general vector spaces , 2002 .

[17]  Chong Li,et al.  On Well Posed Generalized Best Approximation Problems , 2000 .

[18]  J. Aubin.  Optima and Equilibria , 1993 .