Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Mathematical Programming: Series A and B
A proximal-based decomposition method for convex minimization problems
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
A variable-penalty alternating directions method for convex optimization
Mathematical Programming: Series A and B
A Logarithmic-Quadratic Proximal Method for Variational Inequalities
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
A Relative Error Tolerance for a Family of Generalized Proximal Point Methods
Mathematics of Operations Research
Lagrangian Duality and Related Multiplier Methods for Variational Inequality Problems
SIAM Journal on Optimization
Computers & Mathematics with Applications
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The alternating direction method (ADM) is an influential decomposition method for solving a class of variational inequalities with block-separable structures. In the literature, the subproblems of the ADM are usually regularized by quadratic proximal terms to ensure a more stable and attractive numerical performance. In this paper, we propose to apply the logarithmic-quadratic proximal (LQP) terms to regularize the ADM subproblems, and thus develop an LQP-based decomposition method for solving a class of variational inequalities. Global convergence of the new method is proved under standard assumptions.