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On Characterizations of Relatively P– and P0– Properties in Nonsmooth Functions |
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PP: 2841-2847 |
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Author(s) |
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Mohamed A. Tawhid,
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Abstract |
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| For H-differentiable function f from a closed rectangle Q in Rn into Rn, a result of Song, Gowda and Ravindran [On
Characterizations of P- and P0-Properties in Nonsmooth Functions. Mathematics of Operations Research. 25: 400-408 (2000)] asserts
that f is a P(P0)− function on Q if the HQ-differential TQ(x) at each x ∈ Q consisting of P(P0)− matrices. In this paper, we introduce
the concepts of relatively P(P0)− properties in order to extend these results to nonsmooth functions when the underlying functions are
H-differentiable.We give characterizations of relatively P(P0)− of vector nonsmooth functions. Also, our results give characterizations
of relatively P(P0)− when the underlying functions are C1-functions, semismooth-functions, and for locally Lipschitzian functions.
Moreover, we show useful applications of our results by giving illustrations to generalized complementarity problems. |
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