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Reduction and dynamic approach for the multi-choice Shapley value
On the strong convergence of a modified Hestenes-Stiefel method for nonconvex optimization
1. | Department of Mathematics, Changsha University of Science and Technology, Changsha 410004, China, China |
References:
[1] |
M. R. Hestenes and E. L. Stiefel, Method of conjugate gradient for solving linear systems, J. Res. Nat. Bur. Stand., 49 (1952), 409-432. |
[2] |
D. Li and M. Fukushima, A modified BFGS method and its global convergence in nonconvex minimization, J. Comput. Appl. Math., 129 (2001), 15-35.
doi: 10.1016/S0377-0427(00)00540-9. |
[3] |
D. Li and M. Fukushima, On the global convergence of the BFGS method for nonconvex unconstrained optimization problems, SIAM J. Optim., 11 (2001), 1054-1064.
doi: 10.1137/S1052623499354242. |
[4] |
J. J. Moré, B. S. Garbow and K. H. Hillstrom, Testing unconstrained optimization software, ACM Trans. Math. Softw., 7 (1981), 17-41.
doi: 10.1145/355934.355936. |
[5] |
E. Polak and G. Ribière, Note sur la convergence de méthodes de directions conjuguées, Rev. Fr. Inform. Rech. Oper., 16 (1969), 35-43. |
[6] |
B. T. Polyak, The conjugate gradient method in extreme problems, USSR Comput. Math. Math. Phys., 9 (1969), 94-112.
doi: 10.1016/0041-5553(69)90035-4. |
[7] |
L. Zhang, W. Zhou and D. Li, A descent modified Polak-Ribière-Polyak conjugate gradient method and its global convergence, IMA J. Numer. Anal., 26 (2006), 629-640.
doi: 10.1093/imanum/drl016. |
[8] |
L. Zhang, W. Zhou and D. Li, Some descent three-term conjugate gradient methods and their global convergence, Optim. Meth. Softw., 22 (2007), 697-711.
doi: 10.1080/10556780701223293. |
[9] |
W. Zhou and D. Li, On the convergence properties of the unmodified PRP method with a non-descent line search,, submitted., ().
doi: 10.1080/10556788.2013.811241. |
show all references
References:
[1] |
M. R. Hestenes and E. L. Stiefel, Method of conjugate gradient for solving linear systems, J. Res. Nat. Bur. Stand., 49 (1952), 409-432. |
[2] |
D. Li and M. Fukushima, A modified BFGS method and its global convergence in nonconvex minimization, J. Comput. Appl. Math., 129 (2001), 15-35.
doi: 10.1016/S0377-0427(00)00540-9. |
[3] |
D. Li and M. Fukushima, On the global convergence of the BFGS method for nonconvex unconstrained optimization problems, SIAM J. Optim., 11 (2001), 1054-1064.
doi: 10.1137/S1052623499354242. |
[4] |
J. J. Moré, B. S. Garbow and K. H. Hillstrom, Testing unconstrained optimization software, ACM Trans. Math. Softw., 7 (1981), 17-41.
doi: 10.1145/355934.355936. |
[5] |
E. Polak and G. Ribière, Note sur la convergence de méthodes de directions conjuguées, Rev. Fr. Inform. Rech. Oper., 16 (1969), 35-43. |
[6] |
B. T. Polyak, The conjugate gradient method in extreme problems, USSR Comput. Math. Math. Phys., 9 (1969), 94-112.
doi: 10.1016/0041-5553(69)90035-4. |
[7] |
L. Zhang, W. Zhou and D. Li, A descent modified Polak-Ribière-Polyak conjugate gradient method and its global convergence, IMA J. Numer. Anal., 26 (2006), 629-640.
doi: 10.1093/imanum/drl016. |
[8] |
L. Zhang, W. Zhou and D. Li, Some descent three-term conjugate gradient methods and their global convergence, Optim. Meth. Softw., 22 (2007), 697-711.
doi: 10.1080/10556780701223293. |
[9] |
W. Zhou and D. Li, On the convergence properties of the unmodified PRP method with a non-descent line search,, submitted., ().
doi: 10.1080/10556788.2013.811241. |
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