Computational Optimization and Applications

, Volume 69, Issue 2, pp 325–349 | Cite as

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

  • A. Fischer
  • M. Herrich
  • A. F. Izmailov
  • W. Scheck
  • M. V. Solodov


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.


Constrained equation Piecewise smooth equation LP-Newton method Global convergence Quadratic convergence 

Mathematics Subject Classification

90C33 91A10 49M05 49M15 


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Faculty of MathematicsTechnische Universität DresdenDresdenGermany
  2. 2.OR Department, VMK FacultyLomonosov Moscow State University, MSUMoscowRussia
  3. 3.RUDN UniversityMoscowRussia
  4. 4.Department of Mathematic, Physics and Computer SciencesDerzhavin Tambov State University, TSUTambovRussia
  5. 5.IMPA – Instituto de Matemática Pura e AplicadaRio de JaneiroBrazil

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