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A full-Newton step interior-point algorithm for symmetric cone convex quadratic optimization
1. | Department of Mathematics, Shanghai University, 99, Shangda Road, 200444, Shanghai |
2. | Department of Mathematics, Shanghai University, Shanghai 200444, China |
References:
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K. M. Anstreicher, D. den Hertog, C. Roos and T. Terlaky, A long-step barrier method for convex quadratic programming, Algorithmica, 10 (1993), 365-382.
doi: 10.1007/BF01769704. |
[2] |
Y. Q. Bai, M. El Ghami and C. Roos, A comparative study of kernel function for primal-dual interior-point algorithms in linear optimization, SIAM J. Optim., 15 (2004), 101-128.
doi: 10.1137/S1052623403423114. |
[3] |
S. Boyd and L. Vandenberghe, "Convex Optimization," Cambridge University Press, 2004. |
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J. Faraut and A. Korányi, "Analysis on Symmetric Cones," Oxford Mathematical Monographs, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1994. |
[5] |
L. Faybusovich, Linear systems in Jordan algebras and primal-dual interior-point algorithms, Special issue dedicated to William B. Gragg (Monterey, CA, 1996), J. Comput. Appl. Math., 86 (1997), 149-175.
doi: 10.1016/S0377-0427(97)00153-2. |
[6] |
L. Faybusovich, A Jordan-algebraic approach to potential-reduction algorithms, Math. Z., 239 (2002), 117-129.
doi: 10.1007/s002090100286. |
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R. D. C. Monteiro and I. Adler, Interior path following primal-dual algorithms, II: Convex quadratic programming, Math. Program., Ser. A, 44 (1989), 43-66. |
[8] |
Y. E. Nesterov and M. J. Todd, Self-scaled barriers and interior-point methods for convex programming, Math. Oper. Res., 22 (1997), 1-42.
doi: 10.1287/moor.22.1.1. |
[9] |
J. Peng, C. Roos and T. Terlaky, "Self-regularity: A New Paradigm for Primal-Dual Interior-Point Algorithms," Princeton Series in Applied Mathematics, Princeton University Press, Princeton, NJ, 2002. |
[10] |
C. Roos, T. Terlaky and J.-Ph. Vial, "Theory and Algorithms for Linear Optimization. An Interior Point Approach," Wiley-Interscience Series in Discrete Mathematics and Optimization, John Wiley & Sons, Ltd., Chichester, 1997. |
[11] |
S. H. Schmieta and F. Alizadeh, Extension of primal-dual interior point algorithms to symmetric cones, Math. Program, Ser. A, 96 (2003), 409-438. |
[12] |
Changjun Yu, Kok Lay Teo, Liangsheng Zhang and Yanqin Bai, A new exact penalty function method for continuous inequality constrained optimization problems, Journal of Industrial and Management Optimization, 4 (2010), 895-910. |
[13] |
M. V. C. Vieira, "Jordan Algebraic Approach to Symmetric Optimization," Ph.D thesis, Delft University of Technology, 2007. |
show all references
References:
[1] |
K. M. Anstreicher, D. den Hertog, C. Roos and T. Terlaky, A long-step barrier method for convex quadratic programming, Algorithmica, 10 (1993), 365-382.
doi: 10.1007/BF01769704. |
[2] |
Y. Q. Bai, M. El Ghami and C. Roos, A comparative study of kernel function for primal-dual interior-point algorithms in linear optimization, SIAM J. Optim., 15 (2004), 101-128.
doi: 10.1137/S1052623403423114. |
[3] |
S. Boyd and L. Vandenberghe, "Convex Optimization," Cambridge University Press, 2004. |
[4] |
J. Faraut and A. Korányi, "Analysis on Symmetric Cones," Oxford Mathematical Monographs, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1994. |
[5] |
L. Faybusovich, Linear systems in Jordan algebras and primal-dual interior-point algorithms, Special issue dedicated to William B. Gragg (Monterey, CA, 1996), J. Comput. Appl. Math., 86 (1997), 149-175.
doi: 10.1016/S0377-0427(97)00153-2. |
[6] |
L. Faybusovich, A Jordan-algebraic approach to potential-reduction algorithms, Math. Z., 239 (2002), 117-129.
doi: 10.1007/s002090100286. |
[7] |
R. D. C. Monteiro and I. Adler, Interior path following primal-dual algorithms, II: Convex quadratic programming, Math. Program., Ser. A, 44 (1989), 43-66. |
[8] |
Y. E. Nesterov and M. J. Todd, Self-scaled barriers and interior-point methods for convex programming, Math. Oper. Res., 22 (1997), 1-42.
doi: 10.1287/moor.22.1.1. |
[9] |
J. Peng, C. Roos and T. Terlaky, "Self-regularity: A New Paradigm for Primal-Dual Interior-Point Algorithms," Princeton Series in Applied Mathematics, Princeton University Press, Princeton, NJ, 2002. |
[10] |
C. Roos, T. Terlaky and J.-Ph. Vial, "Theory and Algorithms for Linear Optimization. An Interior Point Approach," Wiley-Interscience Series in Discrete Mathematics and Optimization, John Wiley & Sons, Ltd., Chichester, 1997. |
[11] |
S. H. Schmieta and F. Alizadeh, Extension of primal-dual interior point algorithms to symmetric cones, Math. Program, Ser. A, 96 (2003), 409-438. |
[12] |
Changjun Yu, Kok Lay Teo, Liangsheng Zhang and Yanqin Bai, A new exact penalty function method for continuous inequality constrained optimization problems, Journal of Industrial and Management Optimization, 4 (2010), 895-910. |
[13] |
M. V. C. Vieira, "Jordan Algebraic Approach to Symmetric Optimization," Ph.D thesis, Delft University of Technology, 2007. |
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