A globally convergent lp-Newton method

We develop a globally convergent algorithm based on the LP-Newton method, which has been recently proposed for solving constrained equations, possibly nonsmooth and possibly with nonisolated solutions. The new algorithm makes use of linesearch for the natural merit function and preserves the strong local convergence properties of the original LP-Newton scheme. We also present computational experiments on a set of generalized Nash equilibrium problems, and a comparison of our approach with the previous hybrid globalization employing the potential reduction method. © 2016 Society for Industrial and Applied Mathematics.

Authors
Fischer A.1 , Herrich M.1 , Izmailov A.F. 3, 4, 5, 6 , Solodov M.V.2
Journal
SIAM Journal on Optimization
Number of issue
4
Language
English
Pages
2012-2033
Status
Published
Link
External link
DOI
10.1137/15M105241X
Volume
26
Year
2016
Organizations
  • 1 Department of Mathematics, Technische Universiẗat Dresden, Dresden, 01062, Germany
  • 2 IMPA - Instituto Nacional de Mateḿatica Pura E Aplicada, Estrada Dona Castorina 110, Jardim Botanico, Rio de Janeiro, RJ, 22460-320, Brazil
  • 3 Lomonosov Moscow State University, MSU, VMK Faculty, Uchebniy Korpus 2, Russian Federation
  • 4 Department Leninskiye Gory, Moscow, 119991, Russian Federation
  • 5 RUDN University, Moscow, 117198, Russian Federation
  • 6 Department of Mathematic, Physics and Computer Sciences, Derzhavin Tambov State University, TSU, Internationalnaya 33, Tambov, 392000, Russian Federation
Keywords
Constrained equations; Generalized nash equilibrium problems; Global convergence; Lp-Newton method; Quadratic convergence
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/4271/
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