Advanced search
Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 67, 2018 - Issue 11
Submit an article Journal homepage
105
Views
3
CrossRef citations to date
0
Altmetric
Articles

Newton's method for fully parameterized generalized equations

Wei OuyangSchool of Mathematics, Yunnan Normal University, KunmingPeople's Republic of ChinaCorrespondence[email protected]
View further author information
&
Binbin ZhangSchool of Science, Kunming University of Science and Technology, KunmingPeople's Republic of ChinaView further author information
Pages 2061-2080 | Received 27 Feb 2018, Accepted 22 Jul 2018, Published online: 24 Aug 2018

References

  • Robinson SM. Generalized equations and their solutions. I. Basic theory. Point-to-set maps and mathematical programming. Math Program Stud. 1979;10:128–141.
  • Mordukhovich BS. Variational analysis and generalized differentiation, I. Basic theory. II. Applications. Berlin: Springer-Verlag; 2006.
  • Mordukhovich BS, Nghia TTA. Local monotonicity and full stability for parametric variational systems. SIAM J Optim. 2016;26:1032–1059.
  • Mordukhovich BS, Nghia TTA, Pham DT. Full stability of general parametric variational systems. Set-Valued Var Anal. DOI: 10.1007/s11228-018-0474-7.
  • Ouyang W, Zhang B, He Q. Lipschitzian stability of fully parameterized generalized equations. Appl Anal. 2018;97:1717–1729.
  • Uderzo A. On some regularity properties in variational analysis. Set-Valued Anal. 2009;17:409–430.
  • Aragon Artacho FJ, Dontchev AL, Gaydu M, et al. Metric regularity of Newton's iteration. SIAM J Optim. 2011;49:339–362.
  • Dontchev AL, Rockafellar RT. Implicit functions and solution mappings. Berlin: Springer; 2009.
  • Dontchev AL, Rockafellar RT. Robinson's implicit function theorem and its extensions. Math Program, Serie B. 2009;117:129–147.
  • Dontchev AL, Rockafellar RT. Newton's method for generalized equations: a sequential implicit function theorem. Math Program, Serie B. 2010;123:139–159.
  • Robinson SM. Strongly regular generalized equations. Math Oper Res. 1980;5:43–62.
  • Adly S, Cibulka R, Ngai HV. Newton's method for solving inclusions using set-valued approximations. SIAM J Optim. 2015;25:159–184.
  • Adly S, Ngai HV, Nguyen VV. Stability of metric regularity with set-valued perturbations and application to Newton's method for solving generalized equations. Set-Valued Var Anal. 2017;25:543–567.
  • Cibulka R, Dontchev AL, Geoffroy MH. Inexact newton methods and Dennis-Moré theorem for nonsmooth generalized equations. SIAM J Control Optim. 2015;53:1003–1019.
  • Dontchev AL, Rockafellar RT. Convergence of inexact Newton methods for generalized equations. Math Program, Serie B. 2013;139:115–137.
  • Izmailov AF, Solodov MV. Newton-type methods for optimization and variational problems. New York: Springer; 2014.
  • Mordukhovich BS, Ouyang W. Higher-order metric subregularity and its applications. J Glob Optim. 2015;63:777–795.
  • Jourani A, Thibault L. Approximate subdifferential and metric regularity: the finite- dimensional case. Math Program. 1990;47:203–218.
  • Aragon Artacho FJ, Mordukhovich BS. Enhanced metric regularity and Lipschitzian properties of variational systems. J Global Optim. 2011;50:145–167.
  • Dmitruk AB, Kruger AY. Metric regularity and systems of generalized equations. J Math Anal Appl. 2008;342:864–873.
  • Dmitruk AB, Kruger AY. Extensions of metric regularity. Optimization. 2009;58:561–584.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.