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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), 3-51.
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), 101-128.
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, Methods & Applications, 70 (2009), 3584-3602.
doi: 10.1016/j.na.2008.07.016. |
[4] |
Y. Q. Bai, Kernel Function-Based Interior-point Algorithms for Conic Optimization, Science Press, Beijing, 2010. |
[5] |
A. Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization: Analysis, Algorithms and Engineering Applications, MPS/SIAM Series on Optimization, SIAM Publications, Philadelphia, 2001.
doi: 10.1137/1.9780898718829. |
[6] |
I. Bomze, Copositive optimization-Recent developments and applications, European Journal of Operational Research, 216 (2012), 509-520.
doi: 10.1016/j.ejor.2011.04.026. |
[7] |
I. Bomze, M. Dur and C. P. Teo, Copositive optimization, Mathematical Optimization Society Newsletter, Optima 89 (2012), 2-8.
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 IEEE International Conference on, IEEE, (2010), 785-792.
doi: 10.1109/ROBOT.2010.5509833. |
[9] |
S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, Cambridge, 2004.
doi: 10.1017/CBO9780511804441. |
[10] |
S. Boyd and B. Wegbreit, Fast computation of optimal contact forces, IEEE Transactions on Robotics, 23 (2007), 1117-1132. |
[11] |
S. Burer, On the copositive representation of binary and continuous nonconvex quadratic programs, Mathematical Programming Series A, 120 (2009), 479-495.
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, Methods and Applications, 85 (2013), 160-173.
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), 95-117.
doi: 10.1007/s10107-004-0538-3. |
[14] |
S. C. Fang and W. X. Xing, Linear Conic Programming: Theory and Applications, Science Press, Beijing, 2013. |
[15] |
M. Fukushima, Z. Q. Luo and P. Tseng, Smoothing functions for second-order-cone complementarity problems, SIAM Journal on Optimization, 12 (2001), 436-460.
doi: 10.1137/S1052623400380365. |
[16] |
O. Güler, Barrier functions in interior point methods, Mathematics of Operations Research, 21 (1996), 860-885.
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). Available from: http://math.ntnu.edu.tw/~jschen/Publications.html. |
[18] |
B. León, A. Morales and J. Sancho-Bru, Robot Grasping Foundations, In From Robot to Human Grasping Simulation, Springer International Publishing, (2014), 15-31. |
[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), 1460-1473.
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), 499-517.
doi: 10.1007/s13160-012-0081-1. |
[21] |
A. Nemirovski, Advanced in convex optimization: Conic optimization, In International Congress of Mathematicians, 1 (2006), 413-444.
doi: 10.4171/022-1/17. |
[22] |
Y. Nesterov, Towards nonsymmetric conic optimization, Optimization Methods and Software, 27 (2012), 893-917.
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), 324-364.
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), 179-203.
doi: 10.1137/S1052623401383236. |
[25] |
J. Renegar, A Mathematical View of Interior-Point Methods in Convex Optimization, MPS/SIAM Series on Optimization, SIAM Publications, Philadelphia, 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). Available from: http://link.springer.com/journal/10107/onlineFirst/page/1.
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), 895-910.
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), 485-491.
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), 807-816. |
show all references
References:
[1] |
F. Alizadeh and D. Goldfarb, Second-order cone programming, Mathematical Programming Series B, 95 (2003), 3-51.
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), 101-128.
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, Methods & Applications, 70 (2009), 3584-3602.
doi: 10.1016/j.na.2008.07.016. |
[4] |
Y. Q. Bai, Kernel Function-Based Interior-point Algorithms for Conic Optimization, Science Press, Beijing, 2010. |
[5] |
A. Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization: Analysis, Algorithms and Engineering Applications, MPS/SIAM Series on Optimization, SIAM Publications, Philadelphia, 2001.
doi: 10.1137/1.9780898718829. |
[6] |
I. Bomze, Copositive optimization-Recent developments and applications, European Journal of Operational Research, 216 (2012), 509-520.
doi: 10.1016/j.ejor.2011.04.026. |
[7] |
I. Bomze, M. Dur and C. P. Teo, Copositive optimization, Mathematical Optimization Society Newsletter, Optima 89 (2012), 2-8.
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 IEEE International Conference on, IEEE, (2010), 785-792.
doi: 10.1109/ROBOT.2010.5509833. |
[9] |
S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, Cambridge, 2004.
doi: 10.1017/CBO9780511804441. |
[10] |
S. Boyd and B. Wegbreit, Fast computation of optimal contact forces, IEEE Transactions on Robotics, 23 (2007), 1117-1132. |
[11] |
S. Burer, On the copositive representation of binary and continuous nonconvex quadratic programs, Mathematical Programming Series A, 120 (2009), 479-495.
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, Methods and Applications, 85 (2013), 160-173.
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), 95-117.
doi: 10.1007/s10107-004-0538-3. |
[14] |
S. C. Fang and W. X. Xing, Linear Conic Programming: Theory and Applications, Science Press, Beijing, 2013. |
[15] |
M. Fukushima, Z. Q. Luo and P. Tseng, Smoothing functions for second-order-cone complementarity problems, SIAM Journal on Optimization, 12 (2001), 436-460.
doi: 10.1137/S1052623400380365. |
[16] |
O. Güler, Barrier functions in interior point methods, Mathematics of Operations Research, 21 (1996), 860-885.
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). Available from: http://math.ntnu.edu.tw/~jschen/Publications.html. |
[18] |
B. León, A. Morales and J. Sancho-Bru, Robot Grasping Foundations, In From Robot to Human Grasping Simulation, Springer International Publishing, (2014), 15-31. |
[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), 1460-1473.
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), 499-517.
doi: 10.1007/s13160-012-0081-1. |
[21] |
A. Nemirovski, Advanced in convex optimization: Conic optimization, In International Congress of Mathematicians, 1 (2006), 413-444.
doi: 10.4171/022-1/17. |
[22] |
Y. Nesterov, Towards nonsymmetric conic optimization, Optimization Methods and Software, 27 (2012), 893-917.
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), 324-364.
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), 179-203.
doi: 10.1137/S1052623401383236. |
[25] |
J. Renegar, A Mathematical View of Interior-Point Methods in Convex Optimization, MPS/SIAM Series on Optimization, SIAM Publications, Philadelphia, 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). Available from: http://link.springer.com/journal/10107/onlineFirst/page/1.
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), 895-910.
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), 485-491.
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), 807-816. |
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