Interior-point methods based on kernel functions for symmetric optimization

References

• Baes , M. 2007 . Convexity and differentiability properties of spectral functions and spectral mappings on Euclidean Jordan algebras . Linear Algebra Appl. , 422 : 664 – 700 .
   Web of Science ®Google Scholar
• Bai , Y. Q. and Roos , C. 2003 . A polynomial-time algorithm for linear optimization based on a new simple kernel function . Optim. Methods Softw. , 18 ( 6 ) : 631 – 646 .
   Web of Science ®Google Scholar
• Bai , Y. Q. , Roos , C. and El Ghami , M. 2002 . A primal–dual interior-point method for linear optimization based on a new proximity function . Optim. Methods Softw. , 17 ( 6 ) : 985 – 1008 .
   Web of Science ®Google Scholar
• Bai , Y. Q. , El Ghami , M. and Roos , C. 2004 . A comparative study of kernel functions for primal–dual interior-point algorithms in linear optimization . SIAM J. Optim. , 15 ( 1 ) : 101 – 128 . (electronic)
   Web of Science ®Google Scholar
• Dray , T. and Manogue , C. A. 1999 . The exceptional Jordan eigenvalue problem . Int. J. Theoret. Phys. , 38 ( 11 ) : 2901 – 2916 .
   Web of Science ®Google Scholar
• Faraut , J. and Korányi , A. 1994 . Analysis on Symmetric Cones , New York : Oxford Mathematical Monographs, Oxford University Press Inc .
   Google Scholar
• Faybusovich , L. 2002 . A Jordan-algebraic approach to potential-reduction algorithms . Mathematische Zeitschrift , 239 ( 1 ) : 117 – 129 .
   Web of Science ®Google Scholar
• Horn , R. A. and Johnson , C. R. 1991 . Topics in Matrix Analysis , Cambridge : Cambridge University Press .
   Google Scholar
• Jiang , T. 2005 . Algebraic methods for diagonalization of a quaternion matrix in quaternionic quantum theory . J. Math. Phys. , 46 ( 5 ) L052106
   Web of Science ®Google Scholar
• Korányi , A. 1984 . Monotone functions on formally real Jordan algebras . Mathematische Annalen , 269 ( 1 ) : 73 – 76 .
   Web of Science ®Google Scholar
• Lee , H. C. 1949 . Eigenvalues and canonical forms of matrices with quaternion coefficients . Proc. Roy. Irish Acad. Sect. A. , 52 : 253 – 260 .
   Google Scholar
• Luo , Z.-Q. , Sturm , J. F. and Zhang , S. 2000 . Conic convex programming and self-dual embedding . Optim. Methods Softw. , 14 ( 3 ) : 169 – 218 .
   Web of Science ®Google Scholar
• Lütkepohl , H. 1996 . Handbook of Matrices , John Wiley & Sons Ltd .
   Google Scholar
• Marshall , A. W. and Olkin , I. 1979 . Inequalities: Theory of Majorization and Its Applications , New York : Academic Press Inc. [Harcourt Brace Jovanovich Publishers] .
   Google Scholar
• Nesterov , Y. and Nemirovskii , A. 1994 . Interior-point Polynomial Algorithms in Convex Programming , Society for Industrial and Applied Mathematics (SIAM) .
   Google Scholar
• Nesterov , Yu. E. and Todd , M. J. 1997 . Self-scaled barriers and interior-point methods for convex programming . Math. Oper. Res. , 22 ( 1 ) : 1 – 42 .
   Web of Science ®Google Scholar
• Peng , J. , Roos , C. and Terlaky , T. 2001 . A new and efficient large-update interior-point method for linear optimization . Vychislitelnye Tekhnologii. , 6 ( 4 ) : 61 – 80 .
   Google Scholar
• Peng , J. , Roos , C. and Terlaky , T. 2002 . A new class of polynomial primal–dual methods for linear and semidefinite optimization . Eur. J. Oper. Res. , 143 ( 2 ) : 234 – 256 .
   Web of Science ®Google Scholar
• Peng , J. , Roos , C. and Terlaky , T. 2002 . Self-regular functions and new search directions for linear and semidefinite optimization . Math. Program. A , 93 ( 1 ) : 129 – 171 .
   Web of Science ®Google Scholar
• Peng , J. , Roos , C. and Terlaky , T. 2002 . Self-regularity: A New Paradigm for Primal–Dual Interior-point Algorithms , Princeton , NJ : Princeton University Press .
   Google Scholar
• Roos , C. , Terlaky , T. and Vial , J.-Ph. 1997 . Theory and algorithms for linear optimization , Chichester : John Wiley & Sons Ltd .
   Google Scholar
• Schmieta , S. H. and Alizadeh , F. 2003 . Extension of primal–dual interior-point algorithms to symmetric cones . Math. Program. A , 96 ( 3 ) : 409 – 438 .
   Web of Science ®Google Scholar