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A new convergence proof of augmented Lagrangian-based method with full Jacobian decomposition for structured variational inequalities

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  • In the work, we present a new proof for global convergence of a classical method, augmented Lagrangian-based method with full Jacobian decomposition, for a special class of variational inequality problems with a separable structure. This work can be regarded as an improvement to work [14]. The convergence result of the work is established under more general conditions and proven in a new way.
    Mathematics Subject Classification: Primary: 49M27, 65K15, 93B40.


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  • [1]

    S. Dafermos, Traffic Equilibrium and Variational Inequalities, Transportation Science, 14 (1980), 42-54.doi: 10.1287/trsc.14.1.42.


    J. Eckstein and D. P. Bertsekas, On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators, Mathematical Programming, 55 (1992), 293-318.doi: 10.1007/BF01581204.


    M. Fukushima, Application of the alternating direction method of multipliers to separable convex programming problems, Computational Optimization and Applications, 1 (1992), 93-111.doi: 10.1007/BF00247655.


    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), 17-40.


    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), 36-51.doi: 10.1016/j.cam.2013.07.010.


    D. Han and X. Yuan, A Note on the Alternating Direction Method of Multipliers, Journal of Optimization Theory and Applications, 155 (2012), 227-238.doi: 10.1007/s10957-012-0003-z.


    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), 2263-2291.doi: 10.1090/S0025-5718-2014-02829-9.


    P. Harker and J. S. Pang, Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications, Mathematical Programming, 48 (1990), 161-220.doi: 10.1007/BF01582255.


    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.


    B. He, M. Tao, M. Xu and X. Yuan, An alternating direction-based contraction method for linearly constrained separable convex programming problems, Optimization, 62 (2013), 573-596.doi: 10.1080/02331934.2011.611885.


    B. S. He, M. Tao and X.M. Yuan, Alternating direction method with Gaussian-back substitution for separable convex programming, SIAM Journal on Optimization, 22 (2012), 313-340.doi: 10.1137/110822347.


    B. He, M. Tao and X. Yuan, A splitting method for separable convex programming, IMA Journal of Numerical Analysis, 35 (2015), 394-426.doi: 10.1093/imanum/drt060.


    A. Nagurney, Network Economics: A Variational Inequality Approach, Kluwer Academic Publishers, Dordrecht, 1993.doi: 10.1007/978-94-011-2178-1.


    K. Wang, J. Desai and H. He, A note on augmented Lagrangian-based parallel splitting method, Optimization Letters, (2014), 1-14.doi: 10.1007/s11590-014-0825-8.

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