Calculus of Normal Cones and Coderivatives Under the Assumption of  Directional Inner Semicompactness in Asplund Spaces

LONG Pu-jun; YANG Xin-min; WANG Bing-wu

doi:10.21656/1000-0887.370238

Volume 38 Issue 4

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LONG Pu-jun, YANG Xin-min, WANG Bing-wu. Calculus of Normal Cones and Coderivatives Under the Assumption of Directional Inner Semicompactness in Asplund Spaces[J]. Applied Mathematics and Mechanics, 2017, 38(4): 457-468. doi: 10.21656/1000-0887.370238

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Calculus of Normal Cones and Coderivatives Under the Assumption of Directional Inner Semicompactness in Asplund Spaces

doi: 10.21656/1000-0887.370238

Funds: The National Natural Science Foundation of China(Key Program)(11431004)

Received Date: 2016-07-28
Rev Recd Date: 2016-10-17
Publish Date: 2017-04-15

Abstract

Abstract

The directional Mordukhovich normal cones of sets, directional Mordukhovich coderivatives of set-valued mapping, and directional sequential normal compactness of sets and set-valued mapping in the framework of generalized differentiation were studied. Based on the intersection rule for directional Mordukhovich normal cones of sets, the calculus rules on directional Mordukhovich normal cones of sets and directional Mordukhovich coderivatives of set-valued mapping were established under some directional inner semicompactness assumptions. Furthermore, in virtue of the intersection rule for directional sequential normal compactness of sets, the sum rule, inverse mapping rule, and composition rule for directional (partial) sequential normal compactness of sets and set-valued mapping were presented under some directional inner semicompactness assumptions and suitable qualification conditions.

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References

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