The directionally normal cone and optimal condition

Duc Thinh Vo1,
1 Dong Thap University

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Abstract

This paper is devoted to study some properties of the directionally Fréchet normal cones and the directionally limiting normal cones. Moreover, we also modify those directionally limiting normal cones and establish some properties of the modified normal cones. Then we provide some examples to illustrate the differences between these normal cones. Finally, we generate the concepts of the directionally sub-differential via the directionally normal cones. By using the directionally sub-differentials, we come up with a necessary condition for the directionally optimal solution of an optimization problem.

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References

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