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2D system analysis via dual problems and polynomial matrix inequalities
Convergence analysis of a parallel projection algorithm for solving convex feasibility problems
1. | Business School, University of Shanghai for Science and Technology, Shanghai, China |
2. | Department of Health Services and Outcomes Research, National Healthcare Group, 138543 |
3. | Department of Mathematics and Statistics, Curtin University, Perth,WA 6845 |
References:
[1] |
H. H. Bauschke and J. M. Borwein, On projection algorithms for solving convex feasibility problems, SIAM Rev., 38 (1996), 367-426.
doi: 10.1137/S0036144593251710. |
[2] |
H. H. Bauschke, J. M.Borwein, and A. S. Lewis, The method of cyclic projections for closed convex sets in Hilbert space, in Proceedings of the Special Session on Optimization and Nonlinear Analysis, 1995. |
[3] |
S. Boyd, L. EI Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Society for Industrial and Applied Mathematics, Philadlphia, PA, USA, 1994.
doi: 10.1137/1.9781611970777. |
[4] |
Y. Censor and A. Lent, Cyclic subgradient projections, Math. Program., 24 (1982), 233-235.
doi: 10.1007/BF01585107. |
[5] |
Y. Censor, Parallel application of block iterative methods in medical imaging and radiation therapy, Math. Program., 42 (1998), 307-325.
doi: 10.1007/BF01589408. |
[6] |
J. W. Chinneck, The constraint consensus method for finding approximately feasible points in nonlinear programs, INFORMS J. Comput., 16 (2004), 255-265.
doi: 10.1287/ijoc.1030.0046. |
[7] |
P. L. Combeties and S. G. Kruk, Extroplation algorithm for affine-convex feasibility problems, Numer. Algorithms, 41 (2006), 239-274.
doi: 10.1007/s11075-005-9010-6. |
[8] |
Y. Dang and Y. Gao, Non-monotonous accelerated parallel subgradient projection algorithm for convex feasibility problem, Optimization, 63 (2014), 571-584.
doi: 10.1080/02331934.2012.677447. |
[9] |
F. Deutsch, The method of alternating orthogonal projections, Approximation Theory, Spline Functions and Applications, Kluwer Academic Publishers, Dordrecht, 1992. |
[10] |
Y. Gao, Viability criteria for differential inclusions, J. Syst. Sci. Complex., 24 (2011), 825-834.
doi: 10.1007/s11424-011-9056-6. |
[11] |
U. Garcia-palomares, Parallel projected aggregation methods for solving the convex feasibility problem, SIAM J. Optim., 3 (1993), 882-900.
doi: 10.1137/0803046. |
[12] |
U. M. Garcia-Palomares and F. J. Gonzalez-Castano, Incomplete projection algorithms for solving the convex feasibility problem, Numer. Algorithms, 18 (1998), 177-193.
doi: 10.1023/A:1019165330848. |
[13] |
K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, Cambridge Studies in Advanced Mathematics 28, Cambridge University Press, Cambridge, 1990.
doi: 10.1017/CBO9780511526152. |
[14] |
N. I. M. Gould, How good are projection methods for convex feasibility problems, Comput. Optim. Appl., 40 (2008), 1-12.
doi: 10.1007/s10589-007-9073-5. |
[15] |
G. T. Herman, Image Reconstruction From Projections: The Fundamentals of Computerized Tomography, Academic Press, New York, 1980. |
[16] |
K. C. Kiwiel, Block-iterative surrogate projection methods for convex feasibility problem, Linear Algebra Appl., 215 (1995), 225-260.
doi: 10.1016/0024-3795(93)00089-I. |
[17] |
L. Li and Y. Gao, Approximate subgradient projection algorithm for a convex feasibility problem, J. Syst. Eng. Electron., 21 (2010), 527-530. |
[18] |
T. Lucio, A parallel subgradient projections method for the convex feasibility problem, J. Comput. Appl. Math., 18 (1987), 307-320.
doi: 10.1016/0377-0427(87)90004-5. |
[19] |
P. E. Mainge, Convergence theorem for inertial KM-type algorithms, J. Comput. Appl. Math., 219 (2008), 223-236.
doi: 10.1016/j.cam.2007.07.021. |
[20] |
M. Moudafi, Convergence of a splitting inertial proximal method for monotone operators, J. Comput. Appl. Math., 155 (2008), 447-454.
doi: 10.1016/S0377-0427(02)00906-8. |
[21] |
A. Moudafi and E. Elisabeth, An approximate inertial proximal method using enlargement of a maximal monotone operator, Int. J. Pure Appl. Math., 5 (2003), 283-299. |
[22] |
Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Am. Math. Soc., 73 (1967), 591-597. |
[23] |
G. Pierra, Decompasition through formalization in a product space, Math. Program., 28 (1984), 96-115.
doi: 10.1007/BF02612715. |
[24] |
B. T. Polyak, Some methods of speeding up the convergence of iteration method, Zh. Vych. Math., 4 (1964), 791-803. |
show all references
References:
[1] |
H. H. Bauschke and J. M. Borwein, On projection algorithms for solving convex feasibility problems, SIAM Rev., 38 (1996), 367-426.
doi: 10.1137/S0036144593251710. |
[2] |
H. H. Bauschke, J. M.Borwein, and A. S. Lewis, The method of cyclic projections for closed convex sets in Hilbert space, in Proceedings of the Special Session on Optimization and Nonlinear Analysis, 1995. |
[3] |
S. Boyd, L. EI Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Society for Industrial and Applied Mathematics, Philadlphia, PA, USA, 1994.
doi: 10.1137/1.9781611970777. |
[4] |
Y. Censor and A. Lent, Cyclic subgradient projections, Math. Program., 24 (1982), 233-235.
doi: 10.1007/BF01585107. |
[5] |
Y. Censor, Parallel application of block iterative methods in medical imaging and radiation therapy, Math. Program., 42 (1998), 307-325.
doi: 10.1007/BF01589408. |
[6] |
J. W. Chinneck, The constraint consensus method for finding approximately feasible points in nonlinear programs, INFORMS J. Comput., 16 (2004), 255-265.
doi: 10.1287/ijoc.1030.0046. |
[7] |
P. L. Combeties and S. G. Kruk, Extroplation algorithm for affine-convex feasibility problems, Numer. Algorithms, 41 (2006), 239-274.
doi: 10.1007/s11075-005-9010-6. |
[8] |
Y. Dang and Y. Gao, Non-monotonous accelerated parallel subgradient projection algorithm for convex feasibility problem, Optimization, 63 (2014), 571-584.
doi: 10.1080/02331934.2012.677447. |
[9] |
F. Deutsch, The method of alternating orthogonal projections, Approximation Theory, Spline Functions and Applications, Kluwer Academic Publishers, Dordrecht, 1992. |
[10] |
Y. Gao, Viability criteria for differential inclusions, J. Syst. Sci. Complex., 24 (2011), 825-834.
doi: 10.1007/s11424-011-9056-6. |
[11] |
U. Garcia-palomares, Parallel projected aggregation methods for solving the convex feasibility problem, SIAM J. Optim., 3 (1993), 882-900.
doi: 10.1137/0803046. |
[12] |
U. M. Garcia-Palomares and F. J. Gonzalez-Castano, Incomplete projection algorithms for solving the convex feasibility problem, Numer. Algorithms, 18 (1998), 177-193.
doi: 10.1023/A:1019165330848. |
[13] |
K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, Cambridge Studies in Advanced Mathematics 28, Cambridge University Press, Cambridge, 1990.
doi: 10.1017/CBO9780511526152. |
[14] |
N. I. M. Gould, How good are projection methods for convex feasibility problems, Comput. Optim. Appl., 40 (2008), 1-12.
doi: 10.1007/s10589-007-9073-5. |
[15] |
G. T. Herman, Image Reconstruction From Projections: The Fundamentals of Computerized Tomography, Academic Press, New York, 1980. |
[16] |
K. C. Kiwiel, Block-iterative surrogate projection methods for convex feasibility problem, Linear Algebra Appl., 215 (1995), 225-260.
doi: 10.1016/0024-3795(93)00089-I. |
[17] |
L. Li and Y. Gao, Approximate subgradient projection algorithm for a convex feasibility problem, J. Syst. Eng. Electron., 21 (2010), 527-530. |
[18] |
T. Lucio, A parallel subgradient projections method for the convex feasibility problem, J. Comput. Appl. Math., 18 (1987), 307-320.
doi: 10.1016/0377-0427(87)90004-5. |
[19] |
P. E. Mainge, Convergence theorem for inertial KM-type algorithms, J. Comput. Appl. Math., 219 (2008), 223-236.
doi: 10.1016/j.cam.2007.07.021. |
[20] |
M. Moudafi, Convergence of a splitting inertial proximal method for monotone operators, J. Comput. Appl. Math., 155 (2008), 447-454.
doi: 10.1016/S0377-0427(02)00906-8. |
[21] |
A. Moudafi and E. Elisabeth, An approximate inertial proximal method using enlargement of a maximal monotone operator, Int. J. Pure Appl. Math., 5 (2003), 283-299. |
[22] |
Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Am. Math. Soc., 73 (1967), 591-597. |
[23] |
G. Pierra, Decompasition through formalization in a product space, Math. Program., 28 (1984), 96-115.
doi: 10.1007/BF02612715. |
[24] |
B. T. Polyak, Some methods of speeding up the convergence of iteration method, Zh. Vych. Math., 4 (1964), 791-803. |
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