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Continuity and stability of two-stage stochastic programs with quadratic continuous recourse
Primal-dual interior-point algorithms for convex quadratic circular cone optimization
1. | Department of Mathematics, Shanghai University, Shanghai 200444, China, China |
2. | College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai 201620 |
References:
[1] |
F. Alizadeh and D. Goldfard, Second-order cone programming, Math. Program., 95 (2003), 3-51.
doi: 10.1007/s10107-002-0339-5. |
[2] |
M. F. Anjos and J. B. Lasserre, Handbook on Semidefinite, Conic and Polynomial Optimization: Theory, Algorithms, Software and Applications, Internat. Ser. Oper. Res. Management Sci., 166 (2012).
doi: 10.1007/978-1-4614-0769-0. |
[3] |
Y. Q. Bai, Kernel Function-Based Interior-Point Algorithms for Conic Optimization, Science Press, Beijing, 2010. |
[4] |
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 J. Optim., 15 (2004), 101-128.
doi: 10.1137/S1052623403423114. |
[5] |
Y. Q. Bai, G. Q. Wang and C. Roos, Primal-dual interior-point algorithms for second-order cone optimization based on kernel functions, Nonlinear Anal., 70 (2009), 3584-3602.
doi: 10.1016/j.na.2008.07.016. |
[6] |
S. P. Boyd and B. Wegbreit, Fast computation of optimal contact forces, IEEE Trans. Robot., 23 (2007), 1117-1132. |
[7] |
Y. L. Chang, C. Y. Yang and J. S. Chen, Smooth and nonsmooth analysis of vector-valued functions associated with circular cones, Nonlinear Anal., 85 (2013), 160-173.
doi: 10.1016/j.na.2013.01.017. |
[8] |
L. Faybusovich, Euclidean Jordan algebras and interior-point algorithms, Positivity, 1 (1997), 331-357.
doi: 10.1023/A:1009701824047. |
[9] |
G. Gu, M. Zangiabadi and C. Roos, Full Nesterov-Todd step interior-point method for symmetric optimization, European J. Oper. Res., 214(2011), 473-484.
doi: 10.1016/j.ejor.2011.02.022. |
[10] |
Y. Matsukawa and A. Yoshise, A primal barrier function Phase I algorithm for nonsymmetric conic optimization problems, Jpn. J. Ind. Appl. Math., 29 (2012), 499-517.
doi: 10.1007/s13160-012-0081-1. |
[11] |
Y. Nesterov, Towards non-symmetric conic optimization, Optim. Method Softw., 27 (2012) 893-917.
doi: 10.1080/10556788.2011.567270. |
[12] |
J. Peng, C. Roos and T. Terlaky., A new class of polynomial primal-dual interior-point methods for second-order cone optimization based on self-regular proximities, SIAM J. Optim., 13 (2002), 179-203.
doi: 10.1137/S1052623401383236. |
[13] |
C. Roos, T. Terlaky and J.-Ph. Vial, Theory and Algorithms for Linear Optimization: An Interior-Point Approach, John Wiley & Sons, 1997. |
[14] |
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. |
[15] |
A. Skajaa and Y. Y. Ye, A homogeneous interior-point algorithm for nonsymmetric convex conic optimization, Math. Program., 150 (2015), 391-422.
doi: 10.1007/s10107-014-0773-1. |
[16] |
G. Q. Wang and Y. Q. Bai, A primal-dual path-following interior-point algorithm for second-order cone optimization with full Nesterov-Todd step, Appl. Math. Comput., 215 (2009), 1047-1061.
doi: 10.1016/j.amc.2009.06.034. |
[17] |
G. Q. Wang and Y. Q. Bai, Primal-dual interior-point algorithm for convex quadratic semidefinite optimization, Nonlinear Anal., 71 (2009), 3389-3402.
doi: 10.1016/j.na.2009.01.241. |
[18] |
G. Q. Wang and D. T. Zhu, A unified kernel function approach to primal-dual interior-point algorithms for convex quadratic SDO, Numer. Algorithms, 57 (2011), 537-558.
doi: 10.1007/s11075-010-9444-3. |
[19] |
Y. N. Wang, N. H. Xiu and J. Y. Han, On cone of nonsymmetric positive semidefinite matrices, Linear Algebra Appl., 433 (2010), 718-736.
doi: 10.1016/j.laa.2010.03.042. |
[20] |
A. Yoshise and Y. Matsukawa, On optimization over the doubly nonnegative cone, Proceedings of 2010 IEEE Multi-Conference on Systems and Control, (2010), 13-19. |
[21] |
M. Zangiabadi, G. Gu and C. Roos, A full Nesterov-Todd step infeasible interior-point method for second-order cone optimization, J. Optim. Theory Appl., 158 (2013), 816-858.
doi: 10.1007/s10957-013-0278-8. |
[22] |
J. C. Zhou and J. S. Chen, The vector-valued functions associated with circular cones, Abstr. Appl. Anal., 2014 (2014), 21pages.
doi: 10.1155/2014/603542. |
[23] |
J. C. Zhou and J. S. Chen, Properties of circular cone and spectral factorization associated with circular cone, J. Nonlinear Convex Anal., 14 (2013), 807-816. |
[24] |
J. C. Zhou, J. S. Chen and H. F. Hung, Circular cone convexity and some inequalities associated with circular cones, J. Inequal. Appl., 2013 (2013), 17 pages.
doi: 10.1186/1029-242X-2013-571. |
[25] |
J. C. Zhou, J. S. Chen and B. S. Mordukhovich, Variational analysis of circular cone programs, Optim., 64 (2014), 113-147.
doi: 10.1080/02331934.2014.951043. |
show all references
References:
[1] |
F. Alizadeh and D. Goldfard, Second-order cone programming, Math. Program., 95 (2003), 3-51.
doi: 10.1007/s10107-002-0339-5. |
[2] |
M. F. Anjos and J. B. Lasserre, Handbook on Semidefinite, Conic and Polynomial Optimization: Theory, Algorithms, Software and Applications, Internat. Ser. Oper. Res. Management Sci., 166 (2012).
doi: 10.1007/978-1-4614-0769-0. |
[3] |
Y. Q. Bai, Kernel Function-Based Interior-Point Algorithms for Conic Optimization, Science Press, Beijing, 2010. |
[4] |
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 J. Optim., 15 (2004), 101-128.
doi: 10.1137/S1052623403423114. |
[5] |
Y. Q. Bai, G. Q. Wang and C. Roos, Primal-dual interior-point algorithms for second-order cone optimization based on kernel functions, Nonlinear Anal., 70 (2009), 3584-3602.
doi: 10.1016/j.na.2008.07.016. |
[6] |
S. P. Boyd and B. Wegbreit, Fast computation of optimal contact forces, IEEE Trans. Robot., 23 (2007), 1117-1132. |
[7] |
Y. L. Chang, C. Y. Yang and J. S. Chen, Smooth and nonsmooth analysis of vector-valued functions associated with circular cones, Nonlinear Anal., 85 (2013), 160-173.
doi: 10.1016/j.na.2013.01.017. |
[8] |
L. Faybusovich, Euclidean Jordan algebras and interior-point algorithms, Positivity, 1 (1997), 331-357.
doi: 10.1023/A:1009701824047. |
[9] |
G. Gu, M. Zangiabadi and C. Roos, Full Nesterov-Todd step interior-point method for symmetric optimization, European J. Oper. Res., 214(2011), 473-484.
doi: 10.1016/j.ejor.2011.02.022. |
[10] |
Y. Matsukawa and A. Yoshise, A primal barrier function Phase I algorithm for nonsymmetric conic optimization problems, Jpn. J. Ind. Appl. Math., 29 (2012), 499-517.
doi: 10.1007/s13160-012-0081-1. |
[11] |
Y. Nesterov, Towards non-symmetric conic optimization, Optim. Method Softw., 27 (2012) 893-917.
doi: 10.1080/10556788.2011.567270. |
[12] |
J. Peng, C. Roos and T. Terlaky., A new class of polynomial primal-dual interior-point methods for second-order cone optimization based on self-regular proximities, SIAM J. Optim., 13 (2002), 179-203.
doi: 10.1137/S1052623401383236. |
[13] |
C. Roos, T. Terlaky and J.-Ph. Vial, Theory and Algorithms for Linear Optimization: An Interior-Point Approach, John Wiley & Sons, 1997. |
[14] |
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. |
[15] |
A. Skajaa and Y. Y. Ye, A homogeneous interior-point algorithm for nonsymmetric convex conic optimization, Math. Program., 150 (2015), 391-422.
doi: 10.1007/s10107-014-0773-1. |
[16] |
G. Q. Wang and Y. Q. Bai, A primal-dual path-following interior-point algorithm for second-order cone optimization with full Nesterov-Todd step, Appl. Math. Comput., 215 (2009), 1047-1061.
doi: 10.1016/j.amc.2009.06.034. |
[17] |
G. Q. Wang and Y. Q. Bai, Primal-dual interior-point algorithm for convex quadratic semidefinite optimization, Nonlinear Anal., 71 (2009), 3389-3402.
doi: 10.1016/j.na.2009.01.241. |
[18] |
G. Q. Wang and D. T. Zhu, A unified kernel function approach to primal-dual interior-point algorithms for convex quadratic SDO, Numer. Algorithms, 57 (2011), 537-558.
doi: 10.1007/s11075-010-9444-3. |
[19] |
Y. N. Wang, N. H. Xiu and J. Y. Han, On cone of nonsymmetric positive semidefinite matrices, Linear Algebra Appl., 433 (2010), 718-736.
doi: 10.1016/j.laa.2010.03.042. |
[20] |
A. Yoshise and Y. Matsukawa, On optimization over the doubly nonnegative cone, Proceedings of 2010 IEEE Multi-Conference on Systems and Control, (2010), 13-19. |
[21] |
M. Zangiabadi, G. Gu and C. Roos, A full Nesterov-Todd step infeasible interior-point method for second-order cone optimization, J. Optim. Theory Appl., 158 (2013), 816-858.
doi: 10.1007/s10957-013-0278-8. |
[22] |
J. C. Zhou and J. S. Chen, The vector-valued functions associated with circular cones, Abstr. Appl. Anal., 2014 (2014), 21pages.
doi: 10.1155/2014/603542. |
[23] |
J. C. Zhou and J. S. Chen, Properties of circular cone and spectral factorization associated with circular cone, J. Nonlinear Convex Anal., 14 (2013), 807-816. |
[24] |
J. C. Zhou, J. S. Chen and H. F. Hung, Circular cone convexity and some inequalities associated with circular cones, J. Inequal. Appl., 2013 (2013), 17 pages.
doi: 10.1186/1029-242X-2013-571. |
[25] |
J. C. Zhou, J. S. Chen and B. S. Mordukhovich, Variational analysis of circular cone programs, Optim., 64 (2014), 113-147.
doi: 10.1080/02331934.2014.951043. |
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