Variable Metric Primal-Dual Method for Convex Optimization Problems with Changing Constraints

Abstract: We propose a modified primal-dual method for general convex optimization problems with changing affine constraints. We establish convergence of the method that uses variable metric matrices at each iteration. This approach yields new opportunities for control of the parameters according to the constraints changes. In case of the multi-agent optimization problems the method can be adjusted to the changing communication topology and enables the agents to choose the parameters separately of each other. © 2023, Pleiades Publishing, Ltd.