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Positively Homogeneous Functions Revisited

Author

Listed:
  • Valentin V. Gorokhovik

    (National Academy of Sciences of Belarus)

  • Marina Trafimovich

    (Belorussian State University)

Abstract

The paper deals with positively homogeneous functions defined on a finite-dimensional space. Our attention is mainly focused on those subspaces of positively homogeneous functions that are important in nonsmooth analysis and optimization: the subspace of continuous positively homogeneous functions, of Lipschitz continuous positively homogeneous functions, of difference sublinear functions, and of piecewise linear functions. We reproduce some known results and present a number of new ones, in particular, those that concern Lipschitz continuous positively homogeneous functions.

Suggested Citation

  • Valentin V. Gorokhovik & Marina Trafimovich, 2016. "Positively Homogeneous Functions Revisited," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 481-503, November.
    • Handle: RePEc:spr:joptap:v:171:y:2016:i:2:d:10.1007_s10957-016-0891-4
    DOI: 10.1007/s10957-016-0891-4
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    References listed on IDEAS

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    1. M. Abbasov & V. Demyanov, 2013. "Proper and adjoint exhausters in nonsmooth analysis: optimality conditions," Journal of Global Optimization, Springer, vol. 56(2), pages 569-585, June.
    2. Jerzy Grzybowski & Diethard Pallaschke & Ryszard Urbański, 2014. "Demyanov Difference in Infinite-Dimensional Spaces," Springer Optimization and Its Applications, in: Vladimir F. Demyanov & Panos M. Pardalos & Mikhail Batsyn (ed.), Constructive Nonsmooth Analysis and Related Topics, edition 127, pages 13-24, Springer.
    3. M. E. Abbasov & V. F. Demyanov, 2013. "Adjoint Coexhausters in Nonsmooth Analysis and Extremality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 535-553, March.
    4. Jerzy Grzybowski & Diethard Pallaschke & Ryszard Urbański, 2010. "Reduction of finite exhausters," Journal of Global Optimization, Springer, vol. 46(4), pages 589-601, April.
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    Cited by:

    1. Cheikh Toure & Armand Gissler & Anne Auger & Nikolaus Hansen, 2021. "Scaling-invariant Functions versus Positively Homogeneous Functions," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 363-383, October.

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