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Representation of the Clarke Generalized Jacobian via the Quasidifferential

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  • Y. Gao

    (University of Shanghai for Science and Technology)

Abstract

Two differences of convex compact sets in ℜ m× n are proposed. In the light of these differences, representations of the Clarke generalized Jacobian and the B-differential via the quasidifferential are developed for a certain class of functions. These representations can be used to calculate the Clarke generalized Jacobian and the B-differential via the quasidifferential.

Suggested Citation

  • Y. Gao, 2004. "Representation of the Clarke Generalized Jacobian via the Quasidifferential," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 519-532, December.
    • Handle: RePEc:spr:joptap:v:123:y:2004:i:3:d:10.1007_s10957-004-5721-4
    DOI: 10.1007/s10957-004-5721-4
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    References listed on IDEAS

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    1. Y. Gao, 2000. "Demyanov Difference of Two Sets and Optimality Conditions of Lagrange Multiplier Type for Constrained Quasidifferentiable Optimization," Journal of Optimization Theory and Applications, Springer, vol. 104(2), pages 377-394, February.
    2. Jong-Shi Pang & Daniel Ralph, 1996. "Piecewise Smoothness, Local Invertibility, and Parametric Analysis of Normal Maps," Mathematics of Operations Research, INFORMS, vol. 21(2), pages 401-426, May.
    3. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
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    Cited by:

    1. Y. Gao, 2006. "Differences of Polyhedra in Matrix Space and Their Applications to Nonsmooth Analysis," Journal of Optimization Theory and Applications, Springer, vol. 130(3), pages 431-442, September.
    2. Robert Baier & Elza Farkhi & Vera Roshchina, 2016. "From Quasidifferentiable to Directed Subdifferentiable Functions: Exact Calculus Rules," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 384-401, November.

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