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Original Articles

Properties of a Class of Nonlinear Transformations Over Euclidean Jordan Algebras with Applications to Complementarity Problems

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Pages 799-821 | Published online: 16 Jun 2010

REFERENCES

  • M.S. Gowda , R. Sznajder , and J. Tao ( 2004 ). Some P-properties for linear transformations on Euclidean Jordan algebras . Linear Algebra Appl. 393 : 203 – 232 .
  • L.C. Kong , L. Tunçel , and N.H. Xiu ( 2007 ). Monotonicity of Löwner operators and its application to symmetric cone complementarity problems . Math. Oper. Res.
  • L.C. Kong and N.H. Xiu ( 2007 ). New smooth C-functions for symmetric cone complementarity problems . Optim. Lett. 1 : 391 – 400 .
  • Y. Lin and A. Yoshise ( 2005 ). A Homogeneous Model for Mixed Complementarity Problems over Symmetric Cones . Technique Report, Graduate School of Systems and Information Engineering , University of Tsukuba , Tsukuba , Ibaraki , Japan .
  • Y.J. Liu , L.W. Zhang , and Y.H. Wang ( 2006 ). Some properties of a class of merit functions for symmetric cone complementarity problems . Asia-Pacific J. Oper. Res. 23 : 473 – 495 .
  • D. Sun and J. Sun ( 2008 ). Löwner's operator and spectral functions in Euclidean Joedan algebras . Math. Oper. Res. 33 : 421 – 445 .
  • J. Tao and M.S. Gowda ( 2005 ). Some P-properties for nonlinear transformulation on Euclidean Jordan algebras . Math. Oper. Res. 30 ( 4 ): 985 – 1004 .
  • A. Yoshise ( 2006 ). Interior point trajectories and a homogeneous model for nonlinear complementarity problems over symmetric cones . SIAM J. Optim. 17 : 1129 – 1153 .
  • L. Faybusovich ( 1997 ). Euclidean Jordan algebra and interior-point algorithm . Positivity 1 : 331 – 357 .
  • L. Faybusovich ( 1997 ). Linear systems in Jordan algebras and primal-dual interior-point algorithm . J. Comput. Appl. Math. 86 : 149 – 175 .
  • L. Faybusovich and T. Tsuchiya ( 2003 ). Primal-dual algorithms and infinite-dimensional Jordan algebras of finite rank . Math. Program. 97 : 471 – 493 .
  • Z.H. Huang , S.L. Hu , and J. Han (2009). Convergence of a smoothing algorithm for symmetric cone complementarity problems with a nonmonotone line search. Sci. China Ser. A 52(4):833–848.
  • Z.H. Huang and T. Ni ( 2008 ). Smoothing algorithms for complementarity problems over symmetric cones . Comput. Optim. Appl.
  • L.C. Kong , J. Sun , and N.H. Xiu ( 2008 ). A regularized smoothing Newton method for symmetric cone complementarity problems . SIAM J. Optim. 19 : 1028 – 1047 .
  • Y. Lu and Y.X. Yuan ( 2007 ). An interior-point trust region algorithm for general cone progrmming . SIAM J. Optim. 18 : 65 – 86 .
  • S.-H. Pan and J.-S. Chen ( 2009 ). A one-parametric class of merit functions for the symmetric cone complementarity problem . J. Math. Anal. Appl. 335 : 195 – 215 .
  • V. Schmieta and F. Alizadeh ( 2001 ). Associative and Jordan algebras, and polynonial time interior-point algorithms for symmetric cones . Math. Oper. Res. 26 : 543 – 564 .
  • S. Schmieta and F. Alizadeh ( 2003 ). Extension of primal-dual interior-point algorithms to symmetric cones . Math. Program. 96 : 409 – 438 .
  • U. Faraut and A. Korányi ( 1994 ). Analysis on Symmetric Cones . Oxford Mathematical Monographs , Oxford University Press , New York .
  • A. Korányi ( 1984 ). Monotone functions on formally real Jordan algebras . Math. Ann. 269 : 73 – 76 .
  • M.S. Gowda and Y. Song ( 2002 ). Semidefinite Relaxations of Linear Complementarity Problems . Technique Report TRGOW02-01, Department of Mathematics & Statistics , UMBC , Baltimore , MD .
  • X. Chen , H.D. Qi , and P. Tseng ( 2003 ). Analysis of nonsmooth symmetric matrix functions with applications to semidefinite complementarity problems . SIAM J. Optim. 13 : 960 – 985 .
  • F.H. Clarke ( 1983 ). Optimization and Nonsmooth Analysis . Wiley , New York .
  • M.S. Gowda and R. Sznajder ( 2006 ). Automorphism invariance of P and GUS properties of linear transformations in Euclidean Jordan algebras . Math. Oper. Res. 31 : 109 – 123 .
  • D.T. Luc and S. Schaible ( 1996 ). On generalized monotone nonsmooth maps . J. Convex Anal. 3 ( 2 ): 195 – 205 .

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