Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Mathematical Programming: Series A and B
A globally convergent Newton method for solving strongly monotone variational inequalities
Mathematical Programming: Series A and B
A proximal-based decomposition method for convex minimization problems
Mathematical Programming: Series A and B
A variable-penalty alternating directions method for convex optimization
Mathematical Programming: Series A and B
Journal of Optimization Theory and Applications
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The proximal alternating direction method (PADM) solves a kind of structured monotone variational inequalities (VI) via solving a series of lower-dimensional and strongly monotone sub-VIs. We present a new inexact PADM which solves the involved sub-VIs approximately. The new criteria for solving the involved sub-VIs approximately are relaxed than those presented by He et al. [1]. In addition, the new criteria make use of the relative errors of each iteration instead of the absolute errors to control the accuracy of the inexact solutions of the sub-VIs.