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The directional subdifferential of the difference of two convex functions

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  • Jean-Paul Penot

Abstract

We provide a criterion giving a formula for the directional (or contingent) subdifferential of the difference of two convex functions. We even extend it to the difference of two approximately starshaped functions. Our analysis relies on a notion of approximate monotonicity for operators which is much less demanding than the usual one. Copyright Springer Science+Business Media, LLC. 2011

Suggested Citation

  • Jean-Paul Penot, 2011. "The directional subdifferential of the difference of two convex functions," Journal of Global Optimization, Springer, vol. 49(3), pages 505-519, March.
    • Handle: RePEc:spr:jglopt:v:49:y:2011:i:3:p:505-519
    DOI: 10.1007/s10898-010-9615-8
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    References listed on IDEAS

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    1. F. Flores-BAZÁN & W. Oettli, 2001. "Simplified Optimality Conditions for Minimizing the Difference of Vector-Valued Functions," Journal of Optimization Theory and Applications, Springer, vol. 108(3), pages 571-586, March.
    2. Le An & Pham Tao, 2005. "The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems," Annals of Operations Research, Springer, vol. 133(1), pages 23-46, January.
    3. R. Horst & N. V. Thoai, 1999. "DC Programming: Overview," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 1-43, October.
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    Cited by:

    1. S. K. Mishra & Vivek Laha, 2013. "On Approximately Star-Shaped Functions and Approximate Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 278-293, February.
    2. X. L. Guo & S. J. Li, 2014. "Optimality Conditions for Vector Optimization Problems with Difference of Convex Maps," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 821-844, September.
    3. Allahkaram Shafie & Farid Bozorgnia, 2019. "A Note on the Paper “Optimality Conditions for Vector Optimization Problems with Difference of Convex Maps”," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 837-849, August.

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