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A bilevel optimization approach to obtain optimal cost functions for human arm movements
An efficient algorithm for convex quadratic semi-definite optimization
1. | Department of Mathematics, Shanghai University, Shanghai 200444 |
2. | Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, 310018, China |
3. | Department of Mathematics, Zhejiang A&F University, Hangzhou, 311300, China |
References:
[1] |
M. Achache, A new primal-dual path-following method for convex quadratic programming, Computational and Applied Mathematics, 25 (2006), 97-110.
doi: 10.1590/S0101-82052006000100005. |
[2] |
E. Andersen, J. Gondzio, C. Mészáros and X. Xu, "Implementation of Interior Point Methods for Large Scale Linear Programming," Kluwer Acad. Publ., Dordrecht, 1996. |
[3] |
E. Andersen, C. Roos and T. Terlaky, On implementing a primal-dual interior-point method for conic quadratic optimization, Mathematical Programming, 95 (2003), 249-277.
doi: 10.1007/s10107-002-0349-3. |
[4] |
P. Apkarian, D. Noll, J. Thevenet and H. Tuan, A spectral quadratic-SDP method with applications to fixed-order H2 and H∞ synthesis, European Journal of Control, 10 (2004), 527-538.
doi: 10.3166/ejc.10.527-538. |
[5] |
Y. Bai, M. El Ghami and C. Roos, A new efficient large-update primal-dual interior-point method based on a finite barrier, SIAM Journal on Optimization, 13 (2002), 766-782.
doi: 10.1137/S1052623401398132. |
[6] |
Y. 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. |
[7] |
Y. Bai, C. Roos and M. Ghami, A primal-dual interior-point method for linear optimization based on a new proximity function, Optimization Methods and Software, 17 (2002), 985-1008.
doi: 10.1080/1055678021000090024. |
[8] |
I. Bomze, M. Dür, E. De Klerk, C. Roos, A. Quist and T. Terlaky, On copositive programming and standard quadratic optimization problems, Journal of Global Optimization, 18 (2000), 301-320.
doi: 10.1023/A:1026583532263. |
[9] |
Z. Darvay, A weighted-path-following method for linear optimization, Studia Universitatis Babes-Bolyai, Series Informatica, 47 (2002), 3-12. |
[10] |
Z. Darvay, New interior point algorithms in linear programming, Advanced Modeling and Optimization, 5 (2003), 51-92. |
[11] |
E. De Klerk, "Aspects of Semidefinite Programming: Interior Point Algorithms and Selected Applications," Kluwer Academic Publishers, Dordrecht, 2002. |
[12] |
M. El Ghami, "New Primal-Dual Interior-Point Methods Based on Kernel Functions," Ph.D Thesis, Delft University of Technology, 2005. |
[13] |
D. Goldfarb and S. Liu, An O (n3 L) primal interior point algorithm for convex quadratic programming, Mathematical Programming, 49 (1990), 325-340.
doi: 10.1007/BF01588795. |
[14] |
R. Horn and C. Johnson, "Topics in Matrix Analysis," Cambridge Univ Pr, Cambridge, 1994. |
[15] |
M. Kojima, M. Shida and S. Shindoh, Local convergence of predictor—corrector infeasible-interior-point algorithms for SDPs and SDLCPs, Mathematical Programming, 80 (1998), 129-160.
doi: 10.1007/BF01581723. |
[16] |
M. Kojima, S. Shindoh and S. Hara, Interior-point methods for the monotone semidefinite linear complementarity problem in symmetric matrices, SIAM Journal on Optimization, 7 (1997), 86-125.
doi: 10.1137/S1052623494269035. |
[17] |
Y. Lu and Y. Yuan, An interior-point trust-region polynomial algorithm for convex quadratic minimization subject to general convex constraints, Optimization Methods and Software, 23 (2008), 251-258.
doi: 10.1080/10556780701645057. |
[18] |
R. Monteiro and I. Adler, Interior path following primal-dual algorithms. Part II: Convex quadratic programming, Mathematical Programming, 44 (1989), 43-66.
doi: 10.1007/BF01587076. |
[19] |
Y. Nesterov and M. Todd, Primal-dual interior-point methods for self-scaled cones, SIAM Journal on Optimization, 8 (1998), 324-364.
doi: 10.1137/S1052623495290209. |
[20] |
J. Nie and Y. Yuan, A predictor-corrector algorithm for QSDP combining Dikin-Type and Newton centering steps, Annals of Operations Research, 103 (2001), 115-133.
doi: 10.1023/A:1012994820412. |
[21] |
J. Peng, C. Roos and T. Terlaky, New complexity analysis of the primal-dual Newton method for linear optimization, Annals of Operations Research, 99(2000), 23-39.
doi: 10.1023/A:1019280614748. |
[22] |
J. Peng, C. Roos and T. Terlaky, A new and efficient large-update interior-point method for linear optimization, Vychisl. Tekhnol., 6 (2001), 61-80. |
[23] |
J. Peng, C. Roos and T. Terlaky, Self-regular functions and new search directions for linear and semidefinite optimization, Mathematical Programming, 93 (2002), 129-171.
doi: 10.1007/s101070200296. |
[24] |
J. Peng, C. Roos and T. Terlaky, "Self-Regularity: A New Paradigm for Primal-Dual Interior-Point Algorithms," Princeton Univ Pr, NJ, 2002. |
[25] |
J. Sturm and S. Zhang, Symmetric primal-dual path-following algorithms for semidefinite programming, Applied Numerical Mathematics, 29 (1998), 301-315.
doi: 10.1016/S0168-9274(98)00099-3. |
[26] |
J. Sun, On methods for solving nonlinear semidefinite optimization problems, Numerical Algebra, Control and Optimization, 1 (2011), 1-14.
doi: 10.3934/naco.2011.1.1. |
[27] |
M. Todd, K. Toh and R. Tütüncü, On the Nesterov-Todd direction in semidefinite programming, SIAM Journal on Optimization, 8 (1998), 769-796.
doi: 10.1137/S105262349630060X. |
[28] |
K. Toh, R. Tütüncü and M. Todd, Inexact primal-dual path-following algorithms for a special class of convex quadratic SDP and related problems, Pacific J. Optimization, 3 (2007), 135-164. |
[29] |
G. Wang and Y. Bai, A new primal-dual path-following interior-point algorithm for semidefinite optimization, Journal of Mathematical Analysis and Applications, 353 (2009), 339-349.
doi: 10.1016/j.jmaa.2008.12.016. |
[30] |
G. Wang and Y. Bai, Primal-dual interior-point algorithm for convex quadratic semi-definite optimization, Nonlinear Analysis: Theory, Methods & Applications, 71 (2009), 3389-3402. |
[31] |
G. Wang, Y. Bai, Y. Liu and M. Zhang, A new primal-dual interior-point algorithm for convex quadratic optimization, Journal of Shanghai University (English Edition), 12 (2008), 189-196.
doi: 10.1007/s11741-008-0301-3. |
[32] |
H. Wolkowicz, R. Saigal and L. Vandenberghe, "Handbook of Semidefinite Programming: Theory, Algorithms and Applications," Kluwer Academic Publishers, Boston, MA, 2000. |
[33] |
Y. Zhang, On extending some primal-dual interior-point algorithms from linear programming to semidefinite programming, SIAM Journal on Optimization, 8 (1998), 365-386.
doi: 10.1137/S1052623495296115. |
[34] |
L. Zhang and Y. Xu, A new infeasible interior-point algorithm with full step for linear optimization based on a simple function, International Journal of Computer Mathematics, 88 (2011), 3163-3185.
doi: [10.1080/00207160.2011.597503. |
show all references
References:
[1] |
M. Achache, A new primal-dual path-following method for convex quadratic programming, Computational and Applied Mathematics, 25 (2006), 97-110.
doi: 10.1590/S0101-82052006000100005. |
[2] |
E. Andersen, J. Gondzio, C. Mészáros and X. Xu, "Implementation of Interior Point Methods for Large Scale Linear Programming," Kluwer Acad. Publ., Dordrecht, 1996. |
[3] |
E. Andersen, C. Roos and T. Terlaky, On implementing a primal-dual interior-point method for conic quadratic optimization, Mathematical Programming, 95 (2003), 249-277.
doi: 10.1007/s10107-002-0349-3. |
[4] |
P. Apkarian, D. Noll, J. Thevenet and H. Tuan, A spectral quadratic-SDP method with applications to fixed-order H2 and H∞ synthesis, European Journal of Control, 10 (2004), 527-538.
doi: 10.3166/ejc.10.527-538. |
[5] |
Y. Bai, M. El Ghami and C. Roos, A new efficient large-update primal-dual interior-point method based on a finite barrier, SIAM Journal on Optimization, 13 (2002), 766-782.
doi: 10.1137/S1052623401398132. |
[6] |
Y. 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. |
[7] |
Y. Bai, C. Roos and M. Ghami, A primal-dual interior-point method for linear optimization based on a new proximity function, Optimization Methods and Software, 17 (2002), 985-1008.
doi: 10.1080/1055678021000090024. |
[8] |
I. Bomze, M. Dür, E. De Klerk, C. Roos, A. Quist and T. Terlaky, On copositive programming and standard quadratic optimization problems, Journal of Global Optimization, 18 (2000), 301-320.
doi: 10.1023/A:1026583532263. |
[9] |
Z. Darvay, A weighted-path-following method for linear optimization, Studia Universitatis Babes-Bolyai, Series Informatica, 47 (2002), 3-12. |
[10] |
Z. Darvay, New interior point algorithms in linear programming, Advanced Modeling and Optimization, 5 (2003), 51-92. |
[11] |
E. De Klerk, "Aspects of Semidefinite Programming: Interior Point Algorithms and Selected Applications," Kluwer Academic Publishers, Dordrecht, 2002. |
[12] |
M. El Ghami, "New Primal-Dual Interior-Point Methods Based on Kernel Functions," Ph.D Thesis, Delft University of Technology, 2005. |
[13] |
D. Goldfarb and S. Liu, An O (n3 L) primal interior point algorithm for convex quadratic programming, Mathematical Programming, 49 (1990), 325-340.
doi: 10.1007/BF01588795. |
[14] |
R. Horn and C. Johnson, "Topics in Matrix Analysis," Cambridge Univ Pr, Cambridge, 1994. |
[15] |
M. Kojima, M. Shida and S. Shindoh, Local convergence of predictor—corrector infeasible-interior-point algorithms for SDPs and SDLCPs, Mathematical Programming, 80 (1998), 129-160.
doi: 10.1007/BF01581723. |
[16] |
M. Kojima, S. Shindoh and S. Hara, Interior-point methods for the monotone semidefinite linear complementarity problem in symmetric matrices, SIAM Journal on Optimization, 7 (1997), 86-125.
doi: 10.1137/S1052623494269035. |
[17] |
Y. Lu and Y. Yuan, An interior-point trust-region polynomial algorithm for convex quadratic minimization subject to general convex constraints, Optimization Methods and Software, 23 (2008), 251-258.
doi: 10.1080/10556780701645057. |
[18] |
R. Monteiro and I. Adler, Interior path following primal-dual algorithms. Part II: Convex quadratic programming, Mathematical Programming, 44 (1989), 43-66.
doi: 10.1007/BF01587076. |
[19] |
Y. Nesterov and M. Todd, Primal-dual interior-point methods for self-scaled cones, SIAM Journal on Optimization, 8 (1998), 324-364.
doi: 10.1137/S1052623495290209. |
[20] |
J. Nie and Y. Yuan, A predictor-corrector algorithm for QSDP combining Dikin-Type and Newton centering steps, Annals of Operations Research, 103 (2001), 115-133.
doi: 10.1023/A:1012994820412. |
[21] |
J. Peng, C. Roos and T. Terlaky, New complexity analysis of the primal-dual Newton method for linear optimization, Annals of Operations Research, 99(2000), 23-39.
doi: 10.1023/A:1019280614748. |
[22] |
J. Peng, C. Roos and T. Terlaky, A new and efficient large-update interior-point method for linear optimization, Vychisl. Tekhnol., 6 (2001), 61-80. |
[23] |
J. Peng, C. Roos and T. Terlaky, Self-regular functions and new search directions for linear and semidefinite optimization, Mathematical Programming, 93 (2002), 129-171.
doi: 10.1007/s101070200296. |
[24] |
J. Peng, C. Roos and T. Terlaky, "Self-Regularity: A New Paradigm for Primal-Dual Interior-Point Algorithms," Princeton Univ Pr, NJ, 2002. |
[25] |
J. Sturm and S. Zhang, Symmetric primal-dual path-following algorithms for semidefinite programming, Applied Numerical Mathematics, 29 (1998), 301-315.
doi: 10.1016/S0168-9274(98)00099-3. |
[26] |
J. Sun, On methods for solving nonlinear semidefinite optimization problems, Numerical Algebra, Control and Optimization, 1 (2011), 1-14.
doi: 10.3934/naco.2011.1.1. |
[27] |
M. Todd, K. Toh and R. Tütüncü, On the Nesterov-Todd direction in semidefinite programming, SIAM Journal on Optimization, 8 (1998), 769-796.
doi: 10.1137/S105262349630060X. |
[28] |
K. Toh, R. Tütüncü and M. Todd, Inexact primal-dual path-following algorithms for a special class of convex quadratic SDP and related problems, Pacific J. Optimization, 3 (2007), 135-164. |
[29] |
G. Wang and Y. Bai, A new primal-dual path-following interior-point algorithm for semidefinite optimization, Journal of Mathematical Analysis and Applications, 353 (2009), 339-349.
doi: 10.1016/j.jmaa.2008.12.016. |
[30] |
G. Wang and Y. Bai, Primal-dual interior-point algorithm for convex quadratic semi-definite optimization, Nonlinear Analysis: Theory, Methods & Applications, 71 (2009), 3389-3402. |
[31] |
G. Wang, Y. Bai, Y. Liu and M. Zhang, A new primal-dual interior-point algorithm for convex quadratic optimization, Journal of Shanghai University (English Edition), 12 (2008), 189-196.
doi: 10.1007/s11741-008-0301-3. |
[32] |
H. Wolkowicz, R. Saigal and L. Vandenberghe, "Handbook of Semidefinite Programming: Theory, Algorithms and Applications," Kluwer Academic Publishers, Boston, MA, 2000. |
[33] |
Y. Zhang, On extending some primal-dual interior-point algorithms from linear programming to semidefinite programming, SIAM Journal on Optimization, 8 (1998), 365-386.
doi: 10.1137/S1052623495296115. |
[34] |
L. Zhang and Y. Xu, A new infeasible interior-point algorithm with full step for linear optimization based on a simple function, International Journal of Computer Mathematics, 88 (2011), 3163-3185.
doi: [10.1080/00207160.2011.597503. |
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