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Index-proper nonnegative splittings of matrices
Derivatives of eigenvalues and Jordan frames
1. | Departamento de Matemática, Faculdade de Ciências e Tecnologia & CMA, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal |
References:
[1] |
M. Baes, Convexity and differentiability properties of spectral functions and spectral mappings on Euclidean Jordan algebras,, Linear Algebra Appl., 422 (2007), 664.
doi: 10.1016/j.laa.2006.11.025. |
[2] |
Y. Q. Bai, M. El Ghami and C. Roos, A comparative study of kernel functions for primal-dual interior-point algorithms in linear optimization,, SIAM Journal on Optimization, 15 (2004), 101.
doi: 10.1137/S1052623403423114. |
[3] |
J. Faraut and A. Korányi, Analysis on Symmetric Cones,, The Clarendon Press Oxford University Press, (1994).
|
[4] |
L. Faybusovich, Linear systems in Jordan algebras and primal-dual interior-point algorithms,, J. Comput. Appl. Math., 86 (1997), 149.
doi: 10.1016/S0377-0427(97)00153-2. |
[5] |
L. Faybusovich, Euclidean Jordan algebras and interior-point algorithms,, Positivity, 1 (1997), 331.
doi: 10.1023/A:1009701824047. |
[6] |
L. Faybusovich and R. Arana, A long-step primal-dual algorithm for the symmetric programming problem,, Systems Control Lett., 43 (2001), 3.
doi: 10.1016/S0167-6911(01)00092-5. |
[7] |
L. Faybusovich, A Jordan-algebraic approach to potential-reduction algorithms,, Math. Z., 239 (2002), 117.
doi: 10.1007/s002090100286. |
[8] |
G. Gu, M. Zangiabadi and C. Roos, Full Nesterov-Todd step infeasible interior-point method for symmetric optimization,, European Journal of Operational Research, 214 (2011), 473.
doi: 10.1016/j.ejor.2011.02.022. |
[9] |
R. A. Hauser and O. Güler, Self-scaled barrier functions on symmetric cones and their classification,, Found. Comput. Math., 2 (2002), 121.
|
[10] |
R. A. Hauser and Y. Lim, Self-scaled barriers for irreducible symmetric cones,, SIAM J. Optim., 12 (2002), 715.
doi: 10.1137/S1052623400370953. |
[11] |
Z.-H. Huang and T. Ni, Smoothing algorithms for complementarity problems over symmetric cones,, Comput. Optim. Appl., 450 (2010), 557.
doi: 10.1007/s10589-008-9180-y. |
[12] |
B. Kheirfam, A corrector-predictor path-following method for convex quadratic symmetric cone optimization,, Journal of Optimization Theory and Applications, 164 (2015), 246.
doi: 10.1007/s10957-014-0554-2. |
[13] |
M. Kojima and M. Muramatsu, An extension of sums of squares relaxations to polynomial optimization problems over symmetric cones,, Math. Program., 110 (2007), 315.
doi: 10.1007/s10107-006-0004-5. |
[14] |
P. Lancaster, On eigenvalues of matrices dependent on a parameter,, Numer. Math., 6 (1964), 377.
|
[15] |
G. Lesaja and C. Roos, Kernel-based interior-point methods for monotone linear complementarity problems over symmetric cones,, Journal of Optimization Theory and Applications, 150 (2011), 444.
doi: 10.1007/s10957-011-9848-9. |
[16] |
H. Liu, X. Yang and C. Liu, A new wide neighborhood primal-dual infeasible-interior-point method for symmetric cone programming,, Journal of Optimization Theory and Applications, 158 (2013), 796.
doi: 10.1007/s10957-013-0303-y. |
[17] |
Y. Nesterov and A. Nemirovskii, Interior Point Polynomial Algorithms in Convex Programming,, SIAM: Studies in Applied and Numerical Mathematics, (1994).
doi: 10.1137/1.9781611970791. |
[18] |
S. H. Schmieta and F. Alizadeh, Extension of primal-dual interior point algorithms to symmetric cones,, Math. Program., 96 (2003), 409.
doi: 10.1007/s10107-003-0380-z. |
[19] |
S. H. Schmieta and F. Alizadeh, Associative and Jordan algebras, and polynomial time interior-point algorithms for symmetric cones,, Math. Oper. Res., 26 (2001), 543.
doi: 10.1287/moor.26.3.543.10582. |
[20] |
M. V. C. Vieira, Interior-point methods based on kernel functions for symmetric optimization,, Optimization Methods and Software, 27 (2012), 513.
doi: 10.1080/10556788.2010.544877. |
[21] |
G. Q. Wang, C. J. Yub and K. L. Teo, A new full Nesterov-Todd step feasible interior-point method for convex quadratic symmetric cone optimization,, Applied Mathematics and Computation, 221 (2013), 329.
doi: 10.1016/j.amc.2013.06.064. |
[22] |
Z. Yu, Y. Zhu and Q. Cao, On the convergence of central path and generalized proximal point method for symmetric cone linear programming,, Applied Mathematics & Information Sciences, 7 (2103), 2327.
doi: 10.12785/amis/070624. |
show all references
References:
[1] |
M. Baes, Convexity and differentiability properties of spectral functions and spectral mappings on Euclidean Jordan algebras,, Linear Algebra Appl., 422 (2007), 664.
doi: 10.1016/j.laa.2006.11.025. |
[2] |
Y. Q. Bai, M. El Ghami and C. Roos, A comparative study of kernel functions for primal-dual interior-point algorithms in linear optimization,, SIAM Journal on Optimization, 15 (2004), 101.
doi: 10.1137/S1052623403423114. |
[3] |
J. Faraut and A. Korányi, Analysis on Symmetric Cones,, The Clarendon Press Oxford University Press, (1994).
|
[4] |
L. Faybusovich, Linear systems in Jordan algebras and primal-dual interior-point algorithms,, J. Comput. Appl. Math., 86 (1997), 149.
doi: 10.1016/S0377-0427(97)00153-2. |
[5] |
L. Faybusovich, Euclidean Jordan algebras and interior-point algorithms,, Positivity, 1 (1997), 331.
doi: 10.1023/A:1009701824047. |
[6] |
L. Faybusovich and R. Arana, A long-step primal-dual algorithm for the symmetric programming problem,, Systems Control Lett., 43 (2001), 3.
doi: 10.1016/S0167-6911(01)00092-5. |
[7] |
L. Faybusovich, A Jordan-algebraic approach to potential-reduction algorithms,, Math. Z., 239 (2002), 117.
doi: 10.1007/s002090100286. |
[8] |
G. Gu, M. Zangiabadi and C. Roos, Full Nesterov-Todd step infeasible interior-point method for symmetric optimization,, European Journal of Operational Research, 214 (2011), 473.
doi: 10.1016/j.ejor.2011.02.022. |
[9] |
R. A. Hauser and O. Güler, Self-scaled barrier functions on symmetric cones and their classification,, Found. Comput. Math., 2 (2002), 121.
|
[10] |
R. A. Hauser and Y. Lim, Self-scaled barriers for irreducible symmetric cones,, SIAM J. Optim., 12 (2002), 715.
doi: 10.1137/S1052623400370953. |
[11] |
Z.-H. Huang and T. Ni, Smoothing algorithms for complementarity problems over symmetric cones,, Comput. Optim. Appl., 450 (2010), 557.
doi: 10.1007/s10589-008-9180-y. |
[12] |
B. Kheirfam, A corrector-predictor path-following method for convex quadratic symmetric cone optimization,, Journal of Optimization Theory and Applications, 164 (2015), 246.
doi: 10.1007/s10957-014-0554-2. |
[13] |
M. Kojima and M. Muramatsu, An extension of sums of squares relaxations to polynomial optimization problems over symmetric cones,, Math. Program., 110 (2007), 315.
doi: 10.1007/s10107-006-0004-5. |
[14] |
P. Lancaster, On eigenvalues of matrices dependent on a parameter,, Numer. Math., 6 (1964), 377.
|
[15] |
G. Lesaja and C. Roos, Kernel-based interior-point methods for monotone linear complementarity problems over symmetric cones,, Journal of Optimization Theory and Applications, 150 (2011), 444.
doi: 10.1007/s10957-011-9848-9. |
[16] |
H. Liu, X. Yang and C. Liu, A new wide neighborhood primal-dual infeasible-interior-point method for symmetric cone programming,, Journal of Optimization Theory and Applications, 158 (2013), 796.
doi: 10.1007/s10957-013-0303-y. |
[17] |
Y. Nesterov and A. Nemirovskii, Interior Point Polynomial Algorithms in Convex Programming,, SIAM: Studies in Applied and Numerical Mathematics, (1994).
doi: 10.1137/1.9781611970791. |
[18] |
S. H. Schmieta and F. Alizadeh, Extension of primal-dual interior point algorithms to symmetric cones,, Math. Program., 96 (2003), 409.
doi: 10.1007/s10107-003-0380-z. |
[19] |
S. H. Schmieta and F. Alizadeh, Associative and Jordan algebras, and polynomial time interior-point algorithms for symmetric cones,, Math. Oper. Res., 26 (2001), 543.
doi: 10.1287/moor.26.3.543.10582. |
[20] |
M. V. C. Vieira, Interior-point methods based on kernel functions for symmetric optimization,, Optimization Methods and Software, 27 (2012), 513.
doi: 10.1080/10556788.2010.544877. |
[21] |
G. Q. Wang, C. J. Yub and K. L. Teo, A new full Nesterov-Todd step feasible interior-point method for convex quadratic symmetric cone optimization,, Applied Mathematics and Computation, 221 (2013), 329.
doi: 10.1016/j.amc.2013.06.064. |
[22] |
Z. Yu, Y. Zhu and Q. Cao, On the convergence of central path and generalized proximal point method for symmetric cone linear programming,, Applied Mathematics & Information Sciences, 7 (2103), 2327.
doi: 10.12785/amis/070624. |
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