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Global proper efficiency and vector optimization with conearcwise connected setvalued maps
A new convergence proof of augmented Lagrangianbased method with full Jacobian decomposition for structured variational inequalities
1.  Higher Education Key Laboratory of Engineering and Scientific Computing, Taiyuan Normal University, Taiyuan 030012, Shanxi Province, China 
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J. Eckstein and D. P. Bertsekas, On the DouglasRachford splitting method and the proximal point algorithm for maximal monotone operators, Mathematical Programming, 55 (1992), 293318. doi: 10.1007/BF01581204. 
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M. Fukushima, Application of the alternating direction method of multipliers to separable convex programming problems, Computational Optimization and Applications, 1 (1992), 93111. doi: 10.1007/BF00247655. 
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D. Gabay and B. Mercier, A dual algorithm for the solution of nonlinear variational problems via finite element approximations, Computers and Mathematics with Applications, 2 (1976), 1740. 
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D. Han, H. He and L. Xu, A proximal parallel splitting method for minimizing sum of convex functions with linear constraints, Journal of Computational and Applied Mathematics, 256 (2014), 3651. doi: 10.1016/j.cam.2013.07.010. 
[6] 
D. Han and X. Yuan, A Note on the Alternating Direction Method of Multipliers, Journal of Optimization Theory and Applications, 155 (2012), 227238. doi: 10.1007/s109570120003z. 
[7] 
D. Han, X. Yuan and W. Zhang, An augmented Lagrangian based parallel splitting method for separable convex minimization with applications to image processing, Mathematics of Computation, 83 (2014), 22632291. doi: 10.1090/S002557182014028299. 
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P. Harker and J. S. Pang, Finitedimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications, Mathematical Programming, 48 (1990), 161220. doi: 10.1007/BF01582255. 
[9] 
B. He, L. Hou and X. Yuan, On full Jacobian decomposition of the augmented Lagrangian method for separable convex programming, Preprint, 2013. doi: 10.1137/130922793. 
[10] 
B. He, M. Tao, M. Xu and X. Yuan, An alternating directionbased contraction method for linearly constrained separable convex programming problems, Optimization, 62 (2013), 573596. doi: 10.1080/02331934.2011.611885. 
[11] 
B. S. He, M. Tao and X.M. Yuan, Alternating direction method with Gaussianback substitution for separable convex programming, SIAM Journal on Optimization, 22 (2012), 313340. doi: 10.1137/110822347. 
[12] 
B. He, M. Tao and X. Yuan, A splitting method for separable convex programming, IMA Journal of Numerical Analysis, 35 (2015), 394426. doi: 10.1093/imanum/drt060. 
[13] 
A. Nagurney, Network Economics: A Variational Inequality Approach, Kluwer Academic Publishers, Dordrecht, 1993. doi: 10.1007/9789401121781. 
[14] 
K. Wang, J. Desai and H. He, A note on augmented Lagrangianbased parallel splitting method, Optimization Letters, (2014), 114. doi: 10.1007/s1159001408258. 
show all references
References:
[1] 
S. Dafermos, Traffic Equilibrium and Variational Inequalities, Transportation Science, 14 (1980), 4254. doi: 10.1287/trsc.14.1.42. 
[2] 
J. Eckstein and D. P. Bertsekas, On the DouglasRachford splitting method and the proximal point algorithm for maximal monotone operators, Mathematical Programming, 55 (1992), 293318. doi: 10.1007/BF01581204. 
[3] 
M. Fukushima, Application of the alternating direction method of multipliers to separable convex programming problems, Computational Optimization and Applications, 1 (1992), 93111. doi: 10.1007/BF00247655. 
[4] 
D. Gabay and B. Mercier, A dual algorithm for the solution of nonlinear variational problems via finite element approximations, Computers and Mathematics with Applications, 2 (1976), 1740. 
[5] 
D. Han, H. He and L. Xu, A proximal parallel splitting method for minimizing sum of convex functions with linear constraints, Journal of Computational and Applied Mathematics, 256 (2014), 3651. doi: 10.1016/j.cam.2013.07.010. 
[6] 
D. Han and X. Yuan, A Note on the Alternating Direction Method of Multipliers, Journal of Optimization Theory and Applications, 155 (2012), 227238. doi: 10.1007/s109570120003z. 
[7] 
D. Han, X. Yuan and W. Zhang, An augmented Lagrangian based parallel splitting method for separable convex minimization with applications to image processing, Mathematics of Computation, 83 (2014), 22632291. doi: 10.1090/S002557182014028299. 
[8] 
P. Harker and J. S. Pang, Finitedimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications, Mathematical Programming, 48 (1990), 161220. doi: 10.1007/BF01582255. 
[9] 
B. He, L. Hou and X. Yuan, On full Jacobian decomposition of the augmented Lagrangian method for separable convex programming, Preprint, 2013. doi: 10.1137/130922793. 
[10] 
B. He, M. Tao, M. Xu and X. Yuan, An alternating directionbased contraction method for linearly constrained separable convex programming problems, Optimization, 62 (2013), 573596. doi: 10.1080/02331934.2011.611885. 
[11] 
B. S. He, M. Tao and X.M. Yuan, Alternating direction method with Gaussianback substitution for separable convex programming, SIAM Journal on Optimization, 22 (2012), 313340. doi: 10.1137/110822347. 
[12] 
B. He, M. Tao and X. Yuan, A splitting method for separable convex programming, IMA Journal of Numerical Analysis, 35 (2015), 394426. doi: 10.1093/imanum/drt060. 
[13] 
A. Nagurney, Network Economics: A Variational Inequality Approach, Kluwer Academic Publishers, Dordrecht, 1993. doi: 10.1007/9789401121781. 
[14] 
K. Wang, J. Desai and H. He, A note on augmented Lagrangianbased parallel splitting method, Optimization Letters, (2014), 114. doi: 10.1007/s1159001408258. 
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