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The Fermat rule for multifunctions on Banach spaces

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Abstract

Using variational analysis, we study vector optimization problems with objectives being closed multifunctions on Banach spaces or in Asplund spaces. In particular, in terms of the coderivatives, we present Fermat’s rules as necessary conditions for an optimal solution of the above problems. As applications, we also provide some necessary conditions (in terms of Clarke’s normal cones or the limiting normal cones) for Pareto efficient points.

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Authors and Affiliations

  1. Department of Mathematics, Yunnan University, Kunming, 650091, P. R. China

    Xi Yin Zheng

  2. Department of Mathematics, The Chinese University of Hong Kong, Shatin, New Territory, Hong Kong

    Kung Fu Ng

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  1. Xi Yin Zheng
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  2. Kung Fu Ng
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Correspondence to Xi Yin Zheng.

Additional information

This research was supported by a postdoctoral fellowship scheme (CUHK) and an Earmarked Grant from the Research Grant Council of Hong Kong. Research of the first author was also supported by the National Natural Science Foundation of P. R. China (Grant No. 10361008) and the Natural Science Foundation of Yunnan Province, P. R. China (Grant No. 2003A002M).

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Zheng, X., Ng, K. The Fermat rule for multifunctions on Banach spaces. Math. Program. 104, 69–90 (2005). https://doi.org/10.1007/s10107-004-0569-9

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