An Alternate Minimization Method Beyond Positive Definite Proximal Regularization: Convergence And Complexity

In this paper, an alternate minimization method beyond positive definite proximal regularization is introduced for solving linearly constrained separable convex optimization problems. The proposed method can be interpreted as the prediction-correction method from the perspective of variational inequalities. The convergence of the proposed method is established without strong convexity. Finally, the iteration complexity of the proposed method is also derived in the ergodic sense.