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A globally convergent LP-Newton method for piecewise smooth constrained equations: escaping nonstationary accumulation points

Author

Listed:
  • A. Fischer

    (Technische Universität Dresden)

  • M. Herrich

    (Technische Universität Dresden)

  • A. F. Izmailov

    (Lomonosov Moscow State University, MSU
    RUDN University
    Derzhavin Tambov State University, TSU)

  • W. Scheck

    (Technische Universität Dresden)

  • M. V. Solodov

    (IMPA – Instituto de Matemática Pura e Aplicada)

Abstract

The LP-Newton method for constrained equations, introduced some years ago, has powerful properties of local superlinear convergence, covering both possibly nonisolated solutions and possibly nonsmooth equation mappings. A related globally convergent algorithm, based on the LP-Newton subproblems and linesearch for the equation’s infinity norm residual, has recently been developed. In the case of smooth equations, global convergence of this algorithm to B-stationary points of the residual over the constraint set has been shown, which is a natural result: nothing better should generally be expected in variational settings. However, for the piecewise smooth case only a property weaker than B-stationarity could be guaranteed. In this paper, we develop a procedure for piecewise smooth equations that avoids undesirable accumulation points, thus achieving the intended property of B-stationarity.

Suggested Citation

  • A. Fischer & M. Herrich & A. F. Izmailov & W. Scheck & M. V. Solodov, 2018. "A globally convergent LP-Newton method for piecewise smooth constrained equations: escaping nonstationary accumulation points," Computational Optimization and Applications, Springer, vol. 69(2), pages 325-349, March.
    • Handle: RePEc:spr:coopap:v:69:y:2018:i:2:d:10.1007_s10589-017-9950-5
    DOI: 10.1007/s10589-017-9950-5
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    References listed on IDEAS

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    1. Andreas Fischer & Markus Herrich & Alexey Izmailov & Mikhail Solodov, 2016. "Convergence conditions for Newton-type methods applied to complementarity systems with nonisolated solutions," Computational Optimization and Applications, Springer, vol. 63(2), pages 425-459, March.
    2. Francisco Facchinei & Andreas Fischer & Markus Herrich, 2013. "A family of Newton methods for nonsmooth constrained systems with nonisolated solutions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 433-443, June.
    3. Axel Dreves & Francisco Facchinei & Andreas Fischer & Markus Herrich, 2014. "A new error bound result for Generalized Nash Equilibrium Problems and its algorithmic application," Computational Optimization and Applications, Springer, vol. 59(1), pages 63-84, October.
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