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

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. © 2017, Springer Science+Business Media, LLC.

Авторы
Fischer A.1 , Herrich M.1 , Izmailov A.F. 2, 3, 4 , Scheck W.1 , Solodov M.V.5
Издательство
Springer New York LLC
Номер выпуска
2
Язык
Английский
Страницы
325-349
Статус
Опубликовано
Том
69
Год
2018
Организации
  • 1 Faculty of Mathematics, Technische Universität Dresden, Dresden, 01062, Germany
  • 2 OR Department, VMK Faculty, Lomonosov Moscow State University, MSU, Uchebniy Korpus 2, Leninskiye Gory, Moscow, 119991, Russian Federation
  • 3 RUDN University, Miklukho-Maklaya Str. 6, Moscow, 117198, Russian Federation
  • 4 Department of Mathematic, Physics and Computer Sciences, Derzhavin Tambov State University, TSU, Internationalnaya 33, Tambov, 392000, Russian Federation
  • 5 IMPA – Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Jardim Botânico, Rio de Janeiro, RJ 22460-320, Brazil
Ключевые слова
Constrained equation; Global convergence; LP-Newton method; Piecewise smooth equation; Quadratic convergence
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/6819/