A new descent alternating direction method with LQP regularization for the structured variational inequalities
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In this paper, we suggest and analyze a new logarithmic–quadratic proximal alternating direction scheme for the separable constrained convex programming problem. The main contribution of this paper, the predictor is obtained via solving LQP system approximately under significantly relaxed accuracy criterion and the new iterate is obtained by using a new direction with a new step size \(\alpha _k\). Global convergence of the proposed method is proved under certain assumptions. We also reported some numerical results to illustrate the efficiency of the proposed method.
KeywordsVariational inequalities Monotone operator Logarithmic–quadratic proximal method Projection method Alternating direction method
The first author is grateful to Prof. Hafida Bouloiz for her constant help.
- 10.Bnouhachem, A., Ansari, Q.H., Yao, J.C.: SQP alternating direction for structured vriational inequality. J. Nonlinear Convex Anal. 19(3), 461–476 (2018)Google Scholar
- 11.Bnouhachem A., Rassias T.M.: SQP alternating direction method with a new optimal step size for solving variational inequality problems with separable structure. Appl. Anal. Discrete Math. (in Press) Google Scholar
- 15.Gabay, D.: Applications of the method of multipliers to variational inequalities. In: Fortin, M., Glowinski, R. (eds.) Augmented Lagrange Methods: Applications to the Solution of Boundary-valued Problems. Studies in Mathematics and Its Applications, vol. 15, pp. 299–331. North Holland, Amsterdam, The Netherlands (1983)CrossRefGoogle Scholar