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A polynomial-time interior-point method for circular cone programming based on kernel functions
1. | Department of Mathematics, Shanghai University, Shanghai 200444 |
2. | Department of Mathematics, Shanghai University, Shanghai, 200444, China, China |
References:
[1] |
F. Alizadeh and D. Goldfarb, Second-order cone programming,, Mathematical Programming Series B, 95 (2003), 3.
doi: 10.1007/s10107-002-0339-5. |
[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] |
Y. Q. Bai, G. Q. Wang and C. Roos, Primal-dual interior-point algorithms for second-order cone optimization based on kernel functions,, Nonlinear Analysis: Theory, 70 (2009), 3584.
doi: 10.1016/j.na.2008.07.016. |
[4] |
Y. Q. Bai, Kernel Function-Based Interior-point Algorithms for Conic Optimization,, Science Press, (2010). Google Scholar |
[5] |
A. Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization: Analysis, Algorithms and Engineering Applications,, MPS/SIAM Series on Optimization, (2001).
doi: 10.1137/1.9780898718829. |
[6] |
I. Bomze, Copositive optimization-Recent developments and applications,, European Journal of Operational Research, 216 (2012), 509.
doi: 10.1016/j.ejor.2011.04.026. |
[7] |
I. Bomze, M. Dur and C. P. Teo, Copositive optimization,, Mathematical Optimization Society Newsletter, 89 (2012), 2.
doi: 10.1007/978-0-387-74759-0_99. |
[8] |
P. H. Borgstrom, M. A. Batalin, G. Sukhatme, et al., Weighted barrier functions for computation of force distributions with friction cone constraints,, Robotics and Automation (ICRA), (2010), 785.
doi: 10.1109/ROBOT.2010.5509833. |
[9] |
S. Boyd and L. Vandenberghe, Convex Optimization,, Cambridge University Press, (2004).
doi: 10.1017/CBO9780511804441. |
[10] |
S. Boyd and B. Wegbreit, Fast computation of optimal contact forces,, IEEE Transactions on Robotics, 23 (2007), 1117. Google Scholar |
[11] |
S. Burer, On the copositive representation of binary and continuous nonconvex quadratic programs,, Mathematical Programming Series A, 120 (2009), 479.
doi: 10.1007/s10107-008-0223-z. |
[12] |
Y. L. Chang, C. Y. Yang and J. S. Chen, Smooth and nonsmooth analyses of vector-valued functions associated with circular cones,, Nonlinear Analysis: Theory, 85 (2013), 160.
doi: 10.1016/j.na.2013.01.017. |
[13] |
J. S. Chen, X. Chen and P. Tseng, Analysis of nonsmooth vector-valued functions associated with second order cones,, Mathematical Programming Series B, 101 (2004), 95.
doi: 10.1007/s10107-004-0538-3. |
[14] |
S. C. Fang and W. X. Xing, Linear Conic Programming: Theory and Applications,, Science Press, (2013). Google Scholar |
[15] |
M. Fukushima, Z. Q. Luo and P. Tseng, Smoothing functions for second-order-cone complementarity problems,, SIAM Journal on Optimization, 12 (2001), 436.
doi: 10.1137/S1052623400380365. |
[16] |
O. Güler, Barrier functions in interior point methods,, Mathematics of Operations Research, 21 (1996), 860.
doi: 10.1287/moor.21.4.860. |
[17] |
C. H. Ko and J. S. Chen, Optimal grasping manipulation for multifingered robots using semismooth Newton method,, em appear in Mathematical Problems in Engineering, 2013 (2013).
|
[18] |
B. León, A. Morales and J. Sancho-Bru, Robot Grasping Foundations, In From Robot to Human Grasping Simulation,, Springer International Publishing, (2014), 15. Google Scholar |
[19] |
Z. J. Li, S. Z. Sam Ge and S. B. Liu, Contact-force distribution optimization and control for quadruped robots using both gradient and adaptive neural networks,, IEEE Transactions on Neural Networks and Learning Systems, 8 (2014), 1460.
doi: 10.1109/TNNLS.2013.2293500. |
[20] |
Y. Matsukawa and A. Yoshise, A primal barrier function Phase I algorithm for nonsymmetric conic optimization problems,, Japan Journal of Industrial and Applied Mathematics, 29 (2012), 499.
doi: 10.1007/s13160-012-0081-1. |
[21] |
A. Nemirovski, Advanced in convex optimization: Conic optimization,, In International Congress of Mathematicians, 1 (2006), 413.
doi: 10.4171/022-1/17. |
[22] |
Y. Nesterov, Towards nonsymmetric conic optimization,, Optimization Methods and Software, 27 (2012), 893.
doi: 10.1080/10556788.2011.567270. |
[23] |
Y. Nesterov and MJ. Todd, Primal-dual interior-point methods for self-scaled cones,, SIAM Journal on Optimization, 8 (1998), 324.
doi: 10.1137/S1052623495290209. |
[24] |
J. Peng, C. Roos and T. Terlaky, New primal-dual algorithms for second-order conic optimization based on self-regular proximities,, SIAM Journal on Optimization, 13 (2002), 179.
doi: 10.1137/S1052623401383236. |
[25] |
J. Renegar, A Mathematical View of Interior-Point Methods in Convex Optimization,, MPS/SIAM Series on Optimization, (2001).
doi: 10.1137/1.9780898718812. |
[26] |
A. Skajaa and Y. Ye, Homogeneous interior-point algorithm for nonsymmetric convex conic optimization,, To appear mathematical programming, (2014).
doi: 10.1007/s10107-014-0773-1. |
[27] |
C. J. Yu, K. L. Teo, L. S. Zhang and Y. Q. Bai, A new exact penalty function method for continuous inequality constrained optimization problems,, Journal of Industrial Management and Optimization, 6 (2010), 895.
doi: 10.3934/jimo.2010.6.895. |
[28] |
C. J. Yu, K. L. Teo, L. S. Zhang and Y. Q. Bai, On a refinement of the convergence analysis for the new exact penalty function method for continuous inequality constrained optimization problem,, Journal of Industrial Management and Optimization, 8 (2012), 485.
doi: 10.3934/jimo.2012.8.485. |
[29] |
J. C. Zhou and J. S. Chen, Properties of circular cone and spectral factorization associated with circular cone,, Journal of Nonlinear and Convex Analysis, 14 (2014), 807.
|
show all references
References:
[1] |
F. Alizadeh and D. Goldfarb, Second-order cone programming,, Mathematical Programming Series B, 95 (2003), 3.
doi: 10.1007/s10107-002-0339-5. |
[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] |
Y. Q. Bai, G. Q. Wang and C. Roos, Primal-dual interior-point algorithms for second-order cone optimization based on kernel functions,, Nonlinear Analysis: Theory, 70 (2009), 3584.
doi: 10.1016/j.na.2008.07.016. |
[4] |
Y. Q. Bai, Kernel Function-Based Interior-point Algorithms for Conic Optimization,, Science Press, (2010). Google Scholar |
[5] |
A. Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization: Analysis, Algorithms and Engineering Applications,, MPS/SIAM Series on Optimization, (2001).
doi: 10.1137/1.9780898718829. |
[6] |
I. Bomze, Copositive optimization-Recent developments and applications,, European Journal of Operational Research, 216 (2012), 509.
doi: 10.1016/j.ejor.2011.04.026. |
[7] |
I. Bomze, M. Dur and C. P. Teo, Copositive optimization,, Mathematical Optimization Society Newsletter, 89 (2012), 2.
doi: 10.1007/978-0-387-74759-0_99. |
[8] |
P. H. Borgstrom, M. A. Batalin, G. Sukhatme, et al., Weighted barrier functions for computation of force distributions with friction cone constraints,, Robotics and Automation (ICRA), (2010), 785.
doi: 10.1109/ROBOT.2010.5509833. |
[9] |
S. Boyd and L. Vandenberghe, Convex Optimization,, Cambridge University Press, (2004).
doi: 10.1017/CBO9780511804441. |
[10] |
S. Boyd and B. Wegbreit, Fast computation of optimal contact forces,, IEEE Transactions on Robotics, 23 (2007), 1117. Google Scholar |
[11] |
S. Burer, On the copositive representation of binary and continuous nonconvex quadratic programs,, Mathematical Programming Series A, 120 (2009), 479.
doi: 10.1007/s10107-008-0223-z. |
[12] |
Y. L. Chang, C. Y. Yang and J. S. Chen, Smooth and nonsmooth analyses of vector-valued functions associated with circular cones,, Nonlinear Analysis: Theory, 85 (2013), 160.
doi: 10.1016/j.na.2013.01.017. |
[13] |
J. S. Chen, X. Chen and P. Tseng, Analysis of nonsmooth vector-valued functions associated with second order cones,, Mathematical Programming Series B, 101 (2004), 95.
doi: 10.1007/s10107-004-0538-3. |
[14] |
S. C. Fang and W. X. Xing, Linear Conic Programming: Theory and Applications,, Science Press, (2013). Google Scholar |
[15] |
M. Fukushima, Z. Q. Luo and P. Tseng, Smoothing functions for second-order-cone complementarity problems,, SIAM Journal on Optimization, 12 (2001), 436.
doi: 10.1137/S1052623400380365. |
[16] |
O. Güler, Barrier functions in interior point methods,, Mathematics of Operations Research, 21 (1996), 860.
doi: 10.1287/moor.21.4.860. |
[17] |
C. H. Ko and J. S. Chen, Optimal grasping manipulation for multifingered robots using semismooth Newton method,, em appear in Mathematical Problems in Engineering, 2013 (2013).
|
[18] |
B. León, A. Morales and J. Sancho-Bru, Robot Grasping Foundations, In From Robot to Human Grasping Simulation,, Springer International Publishing, (2014), 15. Google Scholar |
[19] |
Z. J. Li, S. Z. Sam Ge and S. B. Liu, Contact-force distribution optimization and control for quadruped robots using both gradient and adaptive neural networks,, IEEE Transactions on Neural Networks and Learning Systems, 8 (2014), 1460.
doi: 10.1109/TNNLS.2013.2293500. |
[20] |
Y. Matsukawa and A. Yoshise, A primal barrier function Phase I algorithm for nonsymmetric conic optimization problems,, Japan Journal of Industrial and Applied Mathematics, 29 (2012), 499.
doi: 10.1007/s13160-012-0081-1. |
[21] |
A. Nemirovski, Advanced in convex optimization: Conic optimization,, In International Congress of Mathematicians, 1 (2006), 413.
doi: 10.4171/022-1/17. |
[22] |
Y. Nesterov, Towards nonsymmetric conic optimization,, Optimization Methods and Software, 27 (2012), 893.
doi: 10.1080/10556788.2011.567270. |
[23] |
Y. Nesterov and MJ. Todd, Primal-dual interior-point methods for self-scaled cones,, SIAM Journal on Optimization, 8 (1998), 324.
doi: 10.1137/S1052623495290209. |
[24] |
J. Peng, C. Roos and T. Terlaky, New primal-dual algorithms for second-order conic optimization based on self-regular proximities,, SIAM Journal on Optimization, 13 (2002), 179.
doi: 10.1137/S1052623401383236. |
[25] |
J. Renegar, A Mathematical View of Interior-Point Methods in Convex Optimization,, MPS/SIAM Series on Optimization, (2001).
doi: 10.1137/1.9780898718812. |
[26] |
A. Skajaa and Y. Ye, Homogeneous interior-point algorithm for nonsymmetric convex conic optimization,, To appear mathematical programming, (2014).
doi: 10.1007/s10107-014-0773-1. |
[27] |
C. J. Yu, K. L. Teo, L. S. Zhang and Y. Q. Bai, A new exact penalty function method for continuous inequality constrained optimization problems,, Journal of Industrial Management and Optimization, 6 (2010), 895.
doi: 10.3934/jimo.2010.6.895. |
[28] |
C. J. Yu, K. L. Teo, L. S. Zhang and Y. Q. Bai, On a refinement of the convergence analysis for the new exact penalty function method for continuous inequality constrained optimization problem,, Journal of Industrial Management and Optimization, 8 (2012), 485.
doi: 10.3934/jimo.2012.8.485. |
[29] |
J. C. Zhou and J. S. Chen, Properties of circular cone and spectral factorization associated with circular cone,, Journal of Nonlinear and Convex Analysis, 14 (2014), 807.
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