Representative of Quasidifferentials and Its Formula for a Quasidifferentiable Function |
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Authors: | Yan Gao |
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Institution: | (1) School of Management, University of Shanghai for Science and Technology, 516 Jungong Road, Shanghai, 200093, P.R. China |
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Abstract: | The quasidifferential of a quasidifferentiable function in the sense of Demyanov and Rubinov is not uniquely defined. Xia
proposed the notion of the kernelled quasidifferential, which is expected to be a representative for the equivalent class
of quasidifferentials. In the 2-dimensional case, the existence of the kernelled quasidifferential was shown. In this paper,
the existence of the kernelled quasidifferential in the n-dimensional space (n>2) is proved under the assumption that the Minkowski difference and the Demyanov difference of subdifferential and minus
superdifferential coincide. In particular, given a quasidifferential, the kernelled quasidifferential can be formulated. Applications
to two classes of generalized separable quasidifferentiable functions are developed.
Mathematics Subject Classifications (2000) 49J52, 54C60, 90C26.
This work was supported by Shanghai Education Committee (04EA01). |
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Keywords: | nonsmooth analysis quasidifferential calculus representative of quasidifferentials nonsmooth optimization |
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