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On a generalization of paramonotone maps and its application to solving the Stampacchia variational inequality

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Pages 593-604 | Received 15 Jul 2005, Accepted 20 Sep 2005, Published online: 29 Oct 2009

References

  • Bruck , RE Jr . 1975 . An iterative solution of a variational inequality for certain monotone operators in Hilbert space, Research announcement . Bulletin of the American Mathematical Society , 81 : 890 – 892 . Bruck Jr, R.E., 1976, Corrigendum.Bulletin of the American Mathematical Society, 82, 353
  • Censor , Y , Iusem , AN and Zenios , SA . 1998 . An interior point method with Bregman functions for the variational inequality problem with paramonotone operators . Mathematical Programming , 81 : 373 – 400 .
  • Iusem , AN . 1998 . On some properties of paramonotone operators . Journal of Convex Analysis , 5 : 269 – 278 .
  • Burachik , R and Iusem , AN . 1998 . A generalized proximal point algorithm for the variational inequality problem in Hilbert space . SIAM Journal on Optimization , 8 : 197 – 216 .
  • Eckstein , J and Ferris , MC . 1999 . Smooth methods of multipliers for complementarity problems . Mathematical Programming , 86 : 65 – 90 .
  • Solodov , MV and Svaiter , BF . 2000 . An inexact hybrid generalized proximal point algorithm and some new results on the theory of Bregman functions . Mathematics of Operations Research , 25 : 214 – 230 .
  • Crouzeix , JP , Marcotte , P and Zhu , D . 2000 . Conditions ensuring the applicability of cutting-plane methods for solving variational inequalities . Mathematical Programming , 88 : 521 – 539 .
  • Wu , Z and Wu , S-Y . 2004 . Weak sharp solutions of variational inequalities in Hilbert spaces . SIAM Journal on Optimization , 14 : 1011 – 1027 .
  • Clarke , FH . 1983 . Optimization and Nonsmooth Analysis , New York : Wiley-Interscience .
  • Rockafellar , T . 1970 . On the maximal monotonicity of subdifferential mappings . Pacific Journal of Mathematics , 33 : 209 – 216 .
  • Hadjisavvas , N , Komlosi , S and Schaible , S . 2005 . Handbook of Generalized Convexity and Generalized Monotonicity , Berlin : Springer .
  • Hadjisavvas , N . 2003 . Continuity and maximality properties of pseudomonotone operators . Journal of Convex Analysis , 10 : 465 – 475 .
  • Hadjisavvas , N . Maximal pseudomonotone operators . Proceedings of the Workshop 'Optimization' . Milano : Datanova Editrice .
  • Daniilidis , A and Hadjisavvas , N . 1999 . On the subdifferentials of pseudoconvex and quasiconvex functions and cyclic monotonicity . Journal of Mathematical Analysis and Applications , 237 : 30 – 42 .
  • Daniilidis , A and Hadjisavvas , N . 2000 . On generalized cyclically monotone operators and proper quasimonotonicity . Optimization , 47 : 123 – 135 .
  • Salmon , G , Strodiot , JJ and Nguyen , VH . 2001 . “ A perturbed auxiliary method for paramonotone multivalued mappings ” . In Advances in Convex Analysis and Global Optimization , Edited by: Hadjisavvas , N and Pardalos , P . Dordrecht : Kluwer .
  • El Farouq , N . 2001 . Pseudomonotone variational inequalities: convergence of proximal methods . Journal of Optimization Theory and Applications , 109 : 311 – 326 .

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