-
Previous Article
Output feedback overlapping control design of interconnected systems with input saturation
- NACO Home
- This Issue
-
Next Article
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), 664-700.
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), 101-128.
doi: 10.1137/S1052623403423114. |
[3] |
J. Faraut and A. Korányi, Analysis on Symmetric Cones, The Clarendon Press Oxford University Press, New York, 1994. |
[4] |
L. Faybusovich, Linear systems in Jordan algebras and primal-dual interior-point algorithms, J. Comput. Appl. Math., 86 (1997), 149-175.
doi: 10.1016/S0377-0427(97)00153-2. |
[5] |
L. Faybusovich, Euclidean Jordan algebras and interior-point algorithms, Positivity, 1 (1997), 331-357.
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), 3-7.
doi: 10.1016/S0167-6911(01)00092-5. |
[7] |
L. Faybusovich, A Jordan-algebraic approach to potential-reduction algorithms, Math. Z., 239 (2002), 117-129.
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), 473-484.
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), 121-143. |
[10] |
R. A. Hauser and Y. Lim, Self-scaled barriers for irreducible symmetric cones, SIAM J. Optim., 12 (2002), 715-723.
doi: 10.1137/S1052623400370953. |
[11] |
Z.-H. Huang and T. Ni, Smoothing algorithms for complementarity problems over symmetric cones, Comput. Optim. Appl., 450 (2010), 557-579.
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), 246-260.
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), 315-336.
doi: 10.1007/s10107-006-0004-5. |
[14] |
P. Lancaster, On eigenvalues of matrices dependent on a parameter, Numer. Math., 6 (1964), 377-387. |
[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), 444-474.
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), 796-815.
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, Philadelphia, 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), 409-438.
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), 543-564.
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), 513-537.
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), 329-343.
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), 2327-2333.
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), 664-700.
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), 101-128.
doi: 10.1137/S1052623403423114. |
[3] |
J. Faraut and A. Korányi, Analysis on Symmetric Cones, The Clarendon Press Oxford University Press, New York, 1994. |
[4] |
L. Faybusovich, Linear systems in Jordan algebras and primal-dual interior-point algorithms, J. Comput. Appl. Math., 86 (1997), 149-175.
doi: 10.1016/S0377-0427(97)00153-2. |
[5] |
L. Faybusovich, Euclidean Jordan algebras and interior-point algorithms, Positivity, 1 (1997), 331-357.
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), 3-7.
doi: 10.1016/S0167-6911(01)00092-5. |
[7] |
L. Faybusovich, A Jordan-algebraic approach to potential-reduction algorithms, Math. Z., 239 (2002), 117-129.
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), 473-484.
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), 121-143. |
[10] |
R. A. Hauser and Y. Lim, Self-scaled barriers for irreducible symmetric cones, SIAM J. Optim., 12 (2002), 715-723.
doi: 10.1137/S1052623400370953. |
[11] |
Z.-H. Huang and T. Ni, Smoothing algorithms for complementarity problems over symmetric cones, Comput. Optim. Appl., 450 (2010), 557-579.
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), 246-260.
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), 315-336.
doi: 10.1007/s10107-006-0004-5. |
[14] |
P. Lancaster, On eigenvalues of matrices dependent on a parameter, Numer. Math., 6 (1964), 377-387. |
[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), 444-474.
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), 796-815.
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, Philadelphia, 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), 409-438.
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), 543-564.
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), 513-537.
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), 329-343.
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), 2327-2333.
doi: 10.12785/amis/070624. |
[1] |
Yu-Lin Chang, Chin-Yu Yang. Some useful inequalities via trace function method in Euclidean Jordan algebras. Numerical Algebra, Control and Optimization, 2014, 4 (1) : 39-48. doi: 10.3934/naco.2014.4.39 |
[2] |
Golamreza Zamani Eskandani, Hamid Vaezi. Hyers--Ulam--Rassias stability of derivations in proper Jordan $CQ^{*}$-algebras. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 1469-1477. doi: 10.3934/dcds.2011.31.1469 |
[3] |
M. P. de Oliveira. On 3-graded Lie algebras, Jordan pairs and the canonical kernel function. Electronic Research Announcements, 2003, 9: 142-151. |
[4] |
Xiao-Hong Liu, Wei Wu. Coerciveness of some merit functions over symmetric cones. Journal of Industrial and Management Optimization, 2009, 5 (3) : 603-613. doi: 10.3934/jimo.2009.5.603 |
[5] |
Vincent Astier, Thomas Unger. Signatures, sums of hermitian squares and positive cones on algebras with involution. Electronic Research Announcements, 2018, 25: 16-26. doi: 10.3934/era.2018.25.003 |
[6] |
Lixing Han. An unconstrained optimization approach for finding real eigenvalues of even order symmetric tensors. Numerical Algebra, Control and Optimization, 2013, 3 (3) : 583-599. doi: 10.3934/naco.2013.3.583 |
[7] |
Xiao-Hong Liu, Wei-Zhe Gu. Smoothing Newton algorithm based on a regularized one-parametric class of smoothing functions for generalized complementarity problems over symmetric cones. Journal of Industrial and Management Optimization, 2010, 6 (2) : 363-380. doi: 10.3934/jimo.2010.6.363 |
[8] |
Brigitte Vallée. Euclidean dynamics. Discrete and Continuous Dynamical Systems, 2006, 15 (1) : 281-352. doi: 10.3934/dcds.2006.15.281 |
[9] |
Thiago Ferraiol, Mauro Patrão, Lucas Seco. Jordan decomposition and dynamics on flag manifolds. Discrete and Continuous Dynamical Systems, 2010, 26 (3) : 923-947. doi: 10.3934/dcds.2010.26.923 |
[10] |
A. A. Kirillov. Family algebras. Electronic Research Announcements, 2000, 6: 7-20. |
[11] |
Víctor Ayala, Adriano Da Silva, Philippe Jouan. Jordan decomposition and the recurrent set of flows of automorphisms. Discrete and Continuous Dynamical Systems, 2021, 41 (4) : 1543-1559. doi: 10.3934/dcds.2020330 |
[12] |
Martin Brokate, Pavel Krejčí. Weak differentiability of scalar hysteresis operators. Discrete and Continuous Dynamical Systems, 2015, 35 (6) : 2405-2421. doi: 10.3934/dcds.2015.35.2405 |
[13] |
Misha Guysinsky, Boris Hasselblatt, Victoria Rayskin. Differentiability of the Hartman--Grobman linearization. Discrete and Continuous Dynamical Systems, 2003, 9 (4) : 979-984. doi: 10.3934/dcds.2003.9.979 |
[14] |
Frédéric Naud. Birkhoff cones, symbolic dynamics and spectrum of transfer operators. Discrete and Continuous Dynamical Systems, 2004, 11 (2&3) : 581-598. doi: 10.3934/dcds.2004.11.581 |
[15] |
Pooja Louhan, S. K. Suneja. On fractional vector optimization over cones with support functions. Journal of Industrial and Management Optimization, 2017, 13 (2) : 549-572. doi: 10.3934/jimo.2016031 |
[16] |
Steffen Konig and Changchang Xi. Cellular algebras and quasi-hereditary algebras: a comparison. Electronic Research Announcements, 1999, 5: 71-75. |
[17] |
A. S. Dzhumadil'daev. Jordan elements and Left-Center of a Free Leibniz algebra. Electronic Research Announcements, 2011, 18: 31-49. doi: 10.3934/era.2011.18.31 |
[18] |
Songting Luo, Leonidas J. Guibas, Hong-Kai Zhao. Euclidean skeletons using closest points. Inverse Problems and Imaging, 2011, 5 (1) : 95-113. doi: 10.3934/ipi.2011.5.95 |
[19] |
Stephen Doty and Anthony Giaquinto. Generators and relations for Schur algebras. Electronic Research Announcements, 2001, 7: 54-62. |
[20] |
Meera G. Mainkar, Cynthia E. Will. Examples of Anosov Lie algebras. Discrete and Continuous Dynamical Systems, 2007, 18 (1) : 39-52. doi: 10.3934/dcds.2007.18.39 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]