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p-regular nonlinearity: tangency at singularity in degenerate optimization problems

Author

Listed:
  • Ewa M. Bednarczuk

    (Systems Research Institute
    Warsaw University of Technology)

  • Alexey Tretyakov

    (Faculty of Sciences
    Dorodnicyn Computing Center of the Russian Academy of Sciences)

Abstract

We investigate description of the tangent cone to the null set of a mapping F at a given point $$x^{*}$$ x ∗ in the case when F is degenerate at $$x^{*}$$ x ∗ . To this aim we introduce the concept of modified 2-regular mappings, which generalizes the concept of p-regular mappings. Our main result provides the description of the tangent cone to the null set of modified 2-regular mappings. With the help of this result we derive new optimality conditions for a wide class of optimization problems with equality constraints.

Suggested Citation

  • Ewa M. Bednarczuk & Alexey Tretyakov, 2017. "p-regular nonlinearity: tangency at singularity in degenerate optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(3), pages 485-500, December.
    • Handle: RePEc:spr:mathme:v:86:y:2017:i:3:d:10.1007_s00186-017-0611-3
    DOI: 10.1007/s00186-017-0611-3
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