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

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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.

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Acknowledgements

We thank the anonymous referees for their valuable reports, whose careful comments and insights have helped a lot to improve the present manuscript.

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Authors and Affiliations

  1. Federal University of Paraná, Curitiba, PR, Brazil

    Letícia Becher

  2. Departamento de Matemática, Universidad de Tarapacá, Casilla 7D, Arica, Chile

    Alberto Ramos

  3. CIEM-CONICET, FAMAF-Universidad Nacional de Córdoba, Córdoba, Argentina

    Damián Fernández

Authors
  1. Letícia Becher
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  2. Damián Fernández
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  3. Alberto Ramos
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Correspondence to Alberto Ramos.

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This work was supported by CNPq (Grant 438185/2018-8, 307270/2019-0), CAPES, CONICET (PIP 11220150100500CO) and SeCyT-UNC (PID 33620180100326CB), FONDECYT regular N\(^{\circ }\) 1231188.

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Becher, L., Fernández, D. & Ramos, A. A trust-region LP-Newton method for constrained nonsmooth equations under Hölder metric subregularity. Comput Optim Appl 86, 711–743 (2023). https://doi.org/10.1007/s10589-023-00498-9

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  • DOI: https://doi.org/10.1007/s10589-023-00498-9

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