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This paper studies distributed algorithms for the extended monotropicoptimization problem, which is a general convex optimization problem with acertain separable structure. The considered objective function is the sum oflocal convex functions assigned to agents in a multi-agent network, withprivate set constraints and affine equality constraints. Each agent only knowsits local objective function, local constraint set, and neighbor information.We propose two novel continuous-time distributed subgradient-based algorithmswith projected output feedback and derivative feedback, respectively, to solvethe extended monotropic optimization problem. Moreover, we show that thealgorithms converge to the optimal solutions under some mild conditions, byvirtue of variational inequalities, Lagrangian methods, decomposition methods,and nonsmooth Lyapunov analysis. Finally, we give two examples to illustratethe applications of the proposed algorithms.

Continuous-Time Distributed Algorithms for Extended Monotropic Optimization Problems