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In this paper, we consider solving a composite optimization problem withcoupling constraints in a multi-agent network based on proximal gradientmethod. In this problem, all the agents jointly minimize the sum of individualcost functions composed of smooth and possibly non-smooth parts. To this end,we derive the dual problem by the concept of Fenchel conjugate, which givesrise to the dual proximal gradient algorithm by allowing for the asymmetricindividual interpretations of the global constraints. Then, an asynchronousdual proximal gradient algorithm is proposed for the asynchronous networks withheterogenous step-sizes and communication delays. For both the two algorithms,if the non-smooth parts of the objective functions are simple-structured, weonly need to update dual variables by some simple operations, accounting forthe reduction of the overall computational complexity. Analytical convergencerate of the proposed algorithms is derived and their efficacy is verified bysolving a social welfare optimization problem of electricity market in thenumerical simulation.

Composite Optimization with Coupling Constraints via Dual Proximal Gradient Method with Applications to Asynchronous Networks