Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 90, 2011 - Issue 6: Variational Analysis and Related Topics
Submit an article Journal homepage
76
Views
11
CrossRef citations to date
0
Altmetric
Original Articles

Fréchet and normal coderivatives of implicit multifunctions

G.M. Lee Department of Applied Mathematics, Pukyong National University, Pusan 608-737, Korea
&
N.D. Yen Institute of Mathematics, Vietnamese Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi 10307, VietnamCorrespondence[email protected]
Pages 1011-1027 | Received 01 Mar 2010, Accepted 01 Apr 2010, Published online: 21 Sep 2010

References

  • Dontchev , AL and Rockafellar , RT . 2009 . “ Implicit Functions and Solution Mappings ” . In A View from Variational Analysis , Dordrecht : Springer .
  • Rudin , W . 1976 . Principles of Mathematical Analysis, , 3rd , New Delhi : McGraw-Hill .
  • Mordukhovich , BS . 2006 . Variational Analysis and Generalized Differentiation, Volume I: Basic Theory, Volume II: Applications , Berlin : Springer .
  • Rockafellar , RT and Wets , RJ-B . 1998 . Variational Analysis , Berlin : Springer .
  • Lee , GM , Tam , NN and Yen , ND . 2008 . Normal coderivative for multifunctions and implicit function theorems . J. Math. Anal. Appl. , 338 : 11 – 22 .
  • Ledyaev , YuS and Zhu , QJ . 1999 . Implicit multifunctions theorems . Set-Valued Anal. , 7 : 209 – 238 .
  • Yen , ND and Yao , J-C . 2009 . Point-based sufficient conditions for metric regularity of implicit multifunctions . Nonlinear Anal. , 70 : 2806 – 2815 .
  • Huy , NQ and Yao , J-C . 2009 . Stability of implicit multifunctions in Asplund spaces . Taiwanese J. Math. , 13 : 47 – 65 .
  • Levy , AB and Mordukhovich , BS . 2004 . Coderivatives in parametric optimization . Math. Program. , 99 : 311 – 327 .
  • Mordukhovich , BS . 2004 . Coderivative analysis of variational systems . J. Global Optim. , 28 : 347 – 362 .
  • L.Q. Thong, Coderivatives of parametric variational systems, Master Thesis (in Vietnamese), Hanoi University of Pedagogy No. 2, November 2008.
  • Mordukhovich , BS . 1980 . Metric approximations and necessary conditions for optimality for general classes of nonsmooth extremal problems (in Russian) . Dokl. Akad. Nauk SSSR , 254 : 1072 – 1076 .
  • Mordukhovich , BS . 1994 . Generalized differential calculus for nonsmooth and set-valued mappings . J. Math. Anal. Appl. , 183 : 250 – 288 .
  • Chieu , NH , Yao , J-C and Yen , ND . 2010 . Relationships between the Robinson robust stability and the Aubin continuity property of implicit multifunctions . Nonlinear Anal. , 72 : 3594 – 3601 .
  • Jeyakumar , V and Yen , ND . 2004 . Solution stability of nonsmooth continuous systems with applications to cone-constrained optimization . SIAM J. Optim. , 14 : 1106 – 1127 .

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.