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

A. Fischer (), M. Herrich (), A. F. Izmailov (), W. Scheck () and M. V. Solodov ()
Additional contact information
A. Fischer: Technische Universität Dresden
M. Herrich: Technische Universität Dresden
A. F. Izmailov: Lomonosov Moscow State University, MSU
W. Scheck: Technische Universität Dresden
M. V. Solodov: IMPA – Instituto de Matemática Pura e Aplicada

Computational Optimization and Applications, 2018, vol. 69, issue 2, No 3, 325-349

Abstract: 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.

Keywords: Constrained equation; Piecewise smooth equation; LP-Newton method; Global convergence; Quadratic convergence; 90C33; 91A10; 49M05; 49M15 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s10589-017-9950-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:69:y:2018:i:2:d:10.1007_s10589-017-9950-5

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-017-9950-5

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().