Abstract
The paper mostly concerns the study of generalized differential properties of the so-called minimal time functions associated, in particular, with constant dynamics and arbitrary closed target sets in control theory. Functions of this type play a significant role in many aspects of optimization, control theory, and Hamilton–Jacobi partial differential equations. We pay the main attention to computing and estimating limiting subgradients of the minimal value functions and to deriving the corresponding relations for Fréchet type ε-subgradients in arbitrary Banach spaces.
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Dedicated to Franco Giannessi in honor of his 75th birthday.
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Mordukhovich, B.S., Nam, N.M. Limiting subgradients of minimal time functions in Banach spaces. J Glob Optim 46, 615–633 (2010). https://doi.org/10.1007/s10898-009-9446-7
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DOI: https://doi.org/10.1007/s10898-009-9446-7
Keywords
- Variational analysis
- Optimization and optimal control
- Hamilton–Jacobi equations
- Minimal time functions
- Minkowski functions
- Generalized differentiation
- Banach spaces