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Simplified Optimality Conditions for Minimizing the Difference of Vector-Valued Functions

Author

Listed:
  • F. Flores-BAZÁN

    (Universidad de Concepción)

  • W. Oettli

    (Universität Mannheim)

Abstract

This paper deals with an axiomatic approach to certain optimality conditions for the vector nonconvex minimization problem min{g(x)−h(x): x∈X}, where X is an arbitrary set and g, h are functions defined on X with values in an ordered topological vector space Z.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:108:y:2001:i:3:d:10.1023_a:1017535424813
    DOI: 10.1023/A:1017535424813
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    Citations

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    Cited by:

    1. 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.
    2. Glaydston Carvalho Bento & Sandro Dimy Barbosa Bitar & João Xavier Cruz Neto & Antoine Soubeyran & João Carlos Oliveira Souza, 2020. "A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems," Computational Optimization and Applications, Springer, vol. 75(1), pages 263-290, January.
    3. Pedro Merino, 2019. "A difference-of-convex functions approach for sparse PDE optimal control problems with nonconvex costs," Computational Optimization and Applications, Springer, vol. 74(1), pages 225-258, September.
    4. Mounir El Maghri, 2015. "( $$\epsilon $$ ϵ -)Efficiency in difference vector optimization," Journal of Global Optimization, Springer, vol. 61(4), pages 803-812, April.
    5. Amos Uderzo, 2023. "Conditions for the stability of ideal efficient solutions in parametric vector optimization via set-valued inclusions," Journal of Global Optimization, Springer, vol. 85(4), pages 917-940, April.
    6. 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.
    7. Yldenilson Torres Almeida & João Xavier Cruz Neto & Paulo Roberto Oliveira & João Carlos de Oliveira Souza, 2020. "A modified proximal point method for DC functions on Hadamard manifolds," Computational Optimization and Applications, Springer, vol. 76(3), pages 649-673, July.

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