Abstract
Some new results which generalize the Hahn-Banach theorem from scalar or vector-valued case to set-valued case are obtained. The existence of the Borwein-strong subgradient and Yang-weak subgradient for set-valued maps are also proven. We present a new Lagrange multiplier theorem and a new Sandwich theorem for set-valued maps.
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Manuscript received: October 2003/Final version received: June 2004
This research was partially supported by the National Science Foundation of China (Grant No. 10171118 and Grant No. 10261005) and Education Commitee project Research Foundation of Chongqing (Grant No. 030801), and the research Commitee of the Hong Kong Polytechnic University.
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Peng, J., Lee, H., Rong, W. et al. Hahn-Banach theorems and subgradients of set-valued maps. Math Meth Oper Res 61, 281–297 (2005). https://doi.org/10.1007/s001860400397
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DOI: https://doi.org/10.1007/s001860400397