Abstract
For a general normed vector space, a special optimal value function called a maximal time function is considered. This covers the farthest distance function as a special case, and has a close relationship with the smallest enclosing ball problem. Some properties of the maximal time function are proven, including the convexity, the lower semicontinuity, and the exact characterizations of its subdifferential formulas.
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Conflict of Interest The authors declare no conflicts of interest.
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Jiang’s research was supported by the National Natural Science Foundation of China (11201324), the Fok Ying Tuny Education Foundation (141114) and the Sichuan Technology Program (2022ZYD0011, 2022NFSC1852).
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Zhou, Z., Jiang, Y. Variational analysis for the maximal time function in normed spaces. Acta Math Sci 44, 1696–1706 (2024). https://doi.org/10.1007/s10473-024-0503-6
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DOI: https://doi.org/10.1007/s10473-024-0503-6