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A trust-region LP-Newton method for constrained nonsmooth equations under Hölder metric subregularity

Author

Listed:
  • Letícia Becher

    (Federal University of Paraná)

  • Damián Fernández

    (CIEM-CONICET, FAMAF-Universidad Nacional de Córdoba)

  • Alberto Ramos

    (Universidad de Tarapacá)

Abstract

We describe and analyze a globally convergent algorithm to find a possible nonisolated zero of a piecewise smooth mapping over a polyhedral set. Such formulation includes Karush–Kuhn–Tucker systems, variational inequalities problems, and generalized Nash equilibrium problems. Our algorithm is based on a modification of the fast locally convergent Linear Programming (LP)-Newton method with a trust-region strategy for globalization that makes use of the natural merit function. The transition between global and local convergence occurs naturally under mild assumption. Our local convergence analysis of the method is performed under a Hölder metric subregularity condition of the mapping defining the possibly nonsmooth equation and the Hölder continuity of the derivative of the selection mapping. We present numerical results that show the feasibility of the approach.

Suggested Citation

  • Letícia Becher & Damián Fernández & Alberto Ramos, 2023. "A trust-region LP-Newton method for constrained nonsmooth equations under Hölder metric subregularity," Computational Optimization and Applications, Springer, vol. 86(2), pages 711-743, November.
    • Handle: RePEc:spr:coopap:v:86:y:2023:i:2:d:10.1007_s10589-023-00498-9
    DOI: 10.1007/s10589-023-00498-9
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    References listed on IDEAS

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    1. Harker, Patrick T., 1991. "Generalized Nash games and quasi-variational inequalities," European Journal of Operational Research, Elsevier, vol. 54(1), pages 81-94, September.
    2. Roberto Andreani & José Mario Martínez & Alberto Ramos & Paulo J. S. Silva, 2018. "Strict Constraint Qualifications and Sequential Optimality Conditions for Constrained Optimization," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 693-717, August.
    3. Koichi Nabetani & Paul Tseng & Masao Fukushima, 2011. "Parametrized variational inequality approaches to generalized Nash equilibrium problems with shared constraints," Computational Optimization and Applications, Springer, vol. 48(3), pages 423-452, April.
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    Cited by:

    1. Andreas Fischer & Alexey F. Izmailov & Mikhail V. Solodov, 2024. "The Levenberg–Marquardt method: an overview of modern convergence theories and more," Computational Optimization and Applications, Springer, vol. 89(1), pages 33-67, September.

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