Approximate Projection Methods for Decentralized Optimization with Functional Constraints

摘要: We consider distributed convex optimization problems that involve a separable objective function and nontrivial functional constraints, such as Linear Matrix Inequalities (LMIs). propose decentralized computationally inexpensive algorithm which is based on the concept of approximate projections. Our one consensus methods in that, at every iteration, each agent performs update its decision variables followed by an step local constraints. Unlike other methods, last our method not Euclidean projection onto feasible set, but instead subgradient direction minimizes constraint violation. two different averaging schemes to mitigate disagreements among agents' estimates. show algorithms converge almost surely, i.e., agrees same optimal solution, under assumption functions are nondifferentiable their subgradients bounded. provide simulation results gossip problem, involves SDP complement theoretical results.