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Distributed Algorithms Involving Fixed Step Size for Mixed Equilibrium Problems With Multiple Set Constraints
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DOI：10.1109/TNNLS.2020.3027288.png)
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Abstract
En 中文
In this brief, the problem of distributively solving a mixed equilibrium problem (EP) with multiple sets is investigated. A network of agents is employed to cooperatively find a point in the intersection of multiple convex sets ensuring that the sum of multiple bifunctions with a free variable is nonnegative. Each agent can only access information associated with its own bifunction and a local convex set. To solve this problem, a distributed algorithm involving a fixed step size is proposed by combining the mirror descent algorithm, the primal-dual algorithm, and the consensus algorithm. Under mild conditions on bifunctions and the graph, we prove that all agents' states asymptotically converge to a solution of the mixed EP. A numerical simulation example is provided for demonstrating the effectiveness of theoretical results.
Keywords:
Optimization
Distributed algorithms
Convergence
Learning systems
Resistance
Electric potential
Mirrors
Distributed algorithm
mixed equilibrium problem (MEP)
multiagent networks
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