Continuous-Time Algorithm Based on Finite-Time Consensus for Distributed Constrained Convex Optimization

This article studies the convex optimization problem with general constraints, where its global objective function is composed of the sum of local objective functions. The objective is to design a distributed algorithm to cooperatively resolve the optimization problem under the condition that only t...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 67; no. 5; pp. 2552 - 2559
Main Authors: Liu, Hongzhe, Zheng, Wei Xing, Yu, Wenwu
Format: Journal Article
Language:English
Published: New York IEEE 01.05.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Computational geometry
Constraints
Convergence
Convex analysis
Convex functions
Convexity
Cost function
Distributed algorithms
Distributed optimization
finite-time consensus
general constraints
Graph theory
Linear programming
Multi-agent systems
Optimization
primal-dual algorithm
Saddle points
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:This article studies the convex optimization problem with general constraints, where its global objective function is composed of the sum of local objective functions. The objective is to design a distributed algorithm to cooperatively resolve the optimization problem under the condition that only the information of each node's own local cost function and its neighbors' states can be obtained. To this end, the optimality condition of the researched optimization problem is developed in terms of the saddle point theory. On this basis, the corresponding continuous-time primal-dual algorithm is constructed for the considered constrained convex optimization problem under time-varying undirected and connected graphs. In the case that the parameters involved in the proposed algorithm satisfy certain inequality, the states of all nodes will reach consensus in finite time. Meanwhile, the average state is globally convergent to the optimal solution of the considered optimization problem under some mild and standard assumptions.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2021.3079192