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Subdifferentials of a perturbed minimal time function in normed spaces

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Abstract

In a general normed vector space, we study the perturbed minimal time function determined by a bounded closed convex set \(U\) and a proper lower semicontinuous function \(f(\cdot )\). In particular, we show that the Fréchet subdifferential and proximal subdifferential of a perturbed minimal time function are representable by virtue of corresponding subdifferential of \(f(\cdot )\) and level sets of the support function of \(U\). Some known results is a special case of these results.

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Acknowledgments

This work was partially supported by National Natural Science Foundation of China (No. 11271274, No. 11126336 and No. 11201324) and New Teacher’s Fund for Doctor Stations, Ministry of Education (No. 20115134120001).

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Authors and Affiliations

  1. Department of Mathematics, Sichuan Normal University, Chengdu, 610066, Sichuan, China

    Yongle Zhang, Yiran He & Yi Jiang

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  1. Yongle Zhang
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  2. Yiran He
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  3. Yi Jiang
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Correspondence to Yongle Zhang.

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Zhang, Y., He, Y. & Jiang, Y. Subdifferentials of a perturbed minimal time function in normed spaces. Optim Lett 8, 1921–1930 (2014). https://doi.org/10.1007/s11590-013-0689-3

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