Publication Cover
Applicable Analysis
An International Journal
Volume 90, 2011 - Issue 5
108
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Projection iterative methods for solving some systems of general nonconvex variational inequalities

Pages 777-786 | Received 05 May 2009, Accepted 22 Oct 2009, Published online: 10 Mar 2011

References

  • Stampacchia , G . 1964 . Formes bilineaires coercivities sur les ensembles convexes . C. R. Acad. Sci. Paris , 258 : 4413 – 4416 .
  • Chang , SS , Lee , HWJ and Chan , CK . 2007 . Generalized system for relaxed cocoercive variational inequalities in Hilbert spaces . Appl. Math. Lett. , 20 : 329 – 334 .
  • Huang , Z and Aslam Noor , M . 2007 . An explicit projection method for a system of nonlinear variational inequalities with different (γ, r)-cocoercive mappings . Appl. Math. Comput. , 190 : 356 – 361 .
  • Aslam Noor , M . 2010 . Some iterative methods for nonconvex variational inequalities . Comput. Math. Model. , (Unpublished work)
  • Aslam Noor , M . 2009 . General nonconvex variational inequalities and applications , Islamabad, , Pakistan : preprint, Mathematics Department, COMSATS Institute of Information Technology .
  • Aslam Noor , M . 2009 . On a system of general mixed variational inequalities . Optim. Lett. , 3 : 437 – 451 .
  • Poliquin , RA , Rockafellar , RT and Thibault , L . 2000 . Local differentiability of distance functions . Trans. Amer. Math. Soc. , 352 : 5231 – 5249 .
  • Aslam Noor , M . 2009 . Projection methods for nonconvex variational inequalities . Optim. Lett. , 3 : 411 – 418 .
  • Aslam Noor , M . 2009 . Implicit iterative methods for nonconvex variational inequalities . J. Optim. Theory Appl. , 143 : 619 – 624 .
  • Aslam Noor , M . 2009 . Iterative methods for general nonconvex variational inequalities . Albanian J. Math. , 3 : 117 – 127 .
  • Aslam Noor , M . 2009 . System of nonconvex variational inequalities . J. Adv. Res. Optim. , 1 : 1 – 10 .
  • Aslam Noor , M . Some new extragradient methods for nonconvex quasi variational inequalities . Nonlin. Anal. Hybrid Syst. , (submitted)
  • Moudafi , A . Projection methods for a system of nonconvex variational inequalities . Nonlin. Anal. , doi: doi: 10.1016/j.na.2008.10.119
  • Clarke , FH , Ledyaev , YS and Wolenski , PR . 1998 . Nonsmooth Analysis and Control Theory , Berlin : Springer-Verlag .
  • Bounkhel , M , Tadj , L and Hamdi , A . 2003 . Iterative schemes to solve nonconvex variational problems . J. Inequal. Pure Appl. Math. , 4 : 1 – 14 .
  • Giannessi , F , Maugeri , A and Pardalos , PM . 2001 . Equilibrium Problems, Nonsmooth Optimization and Variational Inequalities Problems , Dordrecht, Holland : Kluwer Academic Publishers .
  • Glowinski , R , Lions , JL and Tremolieres , R . 1981 . Numerical Analysis of Variational Inequalities , Amsterdam, , Holland : North-Holland .
  • Aslam Noor , M . 1988 . General variational inequalities . Appl. Math. Lett. , 1 : 119 – 121 .
  • Aslam Noor , M . 1999 . Some algorithms for general monotone mixed variational inequalities . Math. Comput. Model. , 29 : 1 – 9 .
  • Aslam Noor , M . 2000 . New approximation schemes for general variational inequalities . J. Math. Anal. Appl. , 251 : 217 – 229 .
  • Aslam Noor , M . 2003 . New extragradient-type methods for general variational inequalities . J. Math. Anal. Appl. , 277 : 379 – 395 .
  • Aslam Noor , M . 2004 . Some developments in general variational inequalities . Appl. Math. Comput. , 152 : 199 – 277 .
  • Aslam Noor , M . 2004 . Iterative schemes for nonconvex variational inequalities . J. Optim. Theory Appl. , 121 : 385 – 395 .
  • Aslam Noor , M . 2006 . Fundamentals of equilibrium problems . Math. Inequal. Appl. , 9 : 529 – 566 .
  • Aslam Noor , M . 2008 . Differentiable nonconvex functions and general variational inequalities . Appl. Math.Comput. , 199 : 623 – 630 .
  • Aslam Noor , M and Inayat Noor , K . 2009 . Projection algorithms for solving a system of general variational inequalities . Nonlin. Anal. , 70 : 2700 – 2706 .
  • Aslam Noor , M and Inayat Noor , K . 2010 . New system of general nonconvex variational inequalities . Appl. Math. E-Notes , 10 (Unpublished work)
  • Aslam Noor , M , Inayat Noor , K and Rassias , ThM . 1993 . Some aspects of variational inequalities . J. Comput. Appl. Math. , 47 : 285 – 312 .
  • Zhu , DL and Marcotte , P . 1996 . Cocoercivity and its role in the convergence of iterative schemes for solving variational inequalities . SIAM J. Optim. , 6 : 614 – 726 .
  • Weng , XL . 1991 . Fixed point iteration for local strictly pseudocontractive mappings . Proc. Amer. Math. Soc. , 113 : 727 – 731 .

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:

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:

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.